Rate and Measurement Problems - SSAT Middle Level Quantitative

1. A bus travels 168 miles in 3.5 hours. At this speed, how far will it travel in 5 hours and 15 minutes?
   Answer: 252 miles This problem tests rate calculations and unit conversions - key skills for distance-speed-time problems. When you see a question asking about traveling at a consistent speed, you need to find the rate first, then apply it to the new time period. Start by finding the bus's speed. Speed equals distance divided by time: $\text{Speed} = \frac{168 \text{ miles}}{3.5 \text{ hours}} = 48 \text{ mph}$ Next, convert 5 hours and 15 minutes to decimal form. Since 15 minutes is $\frac{15}{60} = 0.25$ hours, the total time is 5.25 hours. Now calculate the distance: $\text{Distance} = 48 \text{ mph} \times 5.25 \text{ hours} = 252 \text{ miles}$ Looking at the wrong answers: Choice (A) 225 miles likely comes from incorrectly converting 15 minutes (perhaps using 0.15 instead of 0.25) or making an arithmetic error in the multiplication. Choice (B) 240 miles results from using exactly 5 hours and forgetting to add the extra 15 minutes. Choice (D) 264 miles might come from incorrectly calculating the original speed or making an error in the final multiplication. The correct answer is (C) 252 miles. Strategy tip: Always convert mixed time units to decimals before calculating, and double-check your unit conversions. Remember that 15 minutes = 0.25 hours, 30 minutes = 0.5 hours, and 45 minutes = 0.75 hours - these conversions appear frequently on standardized tests.
2. A factory produces 1,440 widgets in 6 hours. If production continues at the same rate for 8.5 hours, how many widgets will be produced?
   Answer: 2,040 widgets This is a rate problem that tests your ability to find a unit rate and apply it to a different time period. When you see production rates or similar scenarios, your goal is to first determine how much is produced per unit of time. Start by finding the production rate per hour. If 1,440 widgets are produced in 6 hours, divide to get the hourly rate: $1,440 ÷ 6 = 240$ widgets per hour. Now multiply this rate by the new time period: $240 × 8.5 = 2,040$ widgets. Let's examine why the other answers are incorrect. Choice (A) 1,800 widgets results from incorrectly calculating the hourly rate as 300 widgets per hour (perhaps from $1,800 ÷ 6 = 300$), then multiplying $300 × 6 = 1,800$. This suggests the student may have confused the numbers or made an arithmetic error. Choice (B) 1,980 widgets might come from using an incorrect hourly rate of approximately 233 widgets per hour. Choice (D) 2,160 widgets could result from mistakenly using 9 hours instead of 8.5 hours in the final calculation ($240 × 9 = 2,160$). For rate problems on the SSAT, always break them into two clear steps: find the unit rate first, then apply it to the new scenario. Double-check your division when calculating the unit rate, and pay careful attention to decimal values in the problem—8.5 hours, not 8 or 9 hours, was crucial here.
3. A printer can print 15 pages in 2 minutes. At this rate, how long will it take to print a 225-page document?
   Answer: 30 minutes When you encounter a rate problem like this, you're dealing with proportional relationships. The key is to find the printer's rate and then scale it up to the larger job. First, let's establish the printer's rate. If it prints 15 pages in 2 minutes, we can set up a proportion to find how long 225 pages will take: $\frac{15 \text{ pages}}{2 \text{ minutes}} = \frac{225 \text{ pages}}{x \text{ minutes}}$ Cross-multiplying: $15x = 225 \times 2 = 450$ Solving for x: $x = \frac{450}{15} = 30 \text{ minutes}$ Therefore, C) 30 minutes is correct. Let's examine why the other answers are wrong. A) 25 minutes would mean the printer is working faster than its established rate—if you check: 225 ÷ 25 = 9 pages per minute, but the actual rate is only 7.5 pages per minute. B) 28 minutes also assumes a rate that's too fast (about 8 pages per minute). D) 32 minutes assumes the printer is working slower than it actually does (about 7 pages per minute instead of 7.5). For rate problems on the SSAT, always double-check your answer by working backwards. Take your calculated time and see if it produces the original rate: 225 pages ÷ 30 minutes = 7.5 pages per minute, and 15 pages ÷ 2 minutes = 7.5 pages per minute. They match, confirming our answer.
4. A machine produces 144 items in 36 minutes. If the machine operates for 5 hours at the same rate, how many items will it produce?
   Answer: 1,200 items This is a rate problem where you need to find how much work gets done over a different time period. When you see questions about machines, workers, or production at constant rates, always start by finding the rate per unit of time. First, find the machine's rate per minute: $\frac{144 \text{ items}}{36 \text{ minutes}} = 4 \text{ items per minute}$ Next, convert 5 hours to minutes: $5 \text{ hours} \times 60 \text{ minutes per hour} = 300 \text{ minutes}$ Finally, multiply the rate by the total time: $4 \text{ items per minute} \times 300 \text{ minutes} = 1,200 \text{ items}$ Choice A (1,200 items) is correct using this systematic approach. Choice B (1,440 items) likely comes from incorrectly multiplying 144 items by 10 (mistakenly thinking 5 hours is 10 times the original 36 minutes, when it's actually 300 ÷ 36 = 8.33 times longer). Choice C (1,080 items) might result from converting time incorrectly or making an arithmetic error when finding the rate—perhaps using 3 items per minute instead of 4. Choice D (900 items) could come from using an incorrect rate of 3 items per minute, then multiplying by 300 minutes. Study tip: For rate problems, always follow the same three steps: find the rate per unit time, convert all times to the same units, then multiply rate × time. Double-check your unit conversions—mixing up hours and minutes is a common trap on the SSAT.
5. A bicycle wheel makes 150 rotations to travel 300 meters. At this rate, how many rotations will the wheel make to travel 2.4 kilometers?
   Answer: 1,200 rotations This is a rate problem involving proportional relationships. When you encounter questions about consistent rates of travel, rotation, or production, set up a proportion to find the unknown quantity. First, establish the given rate: 150 rotations cover 300 meters. Before setting up your proportion, convert the target distance to the same units. Since 2.4 kilometers equals 2,400 meters, you can now work with consistent units. Set up the proportion: $\frac{150 \text{ rotations}}{300 \text{ meters}} = \frac{x \text{ rotations}}{2400 \text{ meters}}$ Cross-multiply: $150 \times 2400 = 300 \times x$, which gives you $360,000 = 300x$. Solving for x: $x = \frac{360,000}{300} = 1,200$ rotations. Looking at the wrong answers: Choice (A) 900 rotations likely comes from incorrectly calculating the rate as 1 rotation per 2 meters instead of the correct rate of 1 rotation per 2 meters, then making an arithmetic error. Choice (B) 1,080 rotations might result from converting kilometers incorrectly or making calculation mistakes during cross-multiplication. Choice (D) 1,350 rotations could come from setting up the proportion incorrectly or computational errors. The key strategy for rate problems is always converting to consistent units first, then setting up your proportion carefully. Double-check your unit conversion (2.4 km = 2,400 m) and your arithmetic. These problems test both your proportional reasoning skills and attention to detail with units.
6. Sarah can type 450 words in 15 minutes. At this same rate, how many words can she type in 2 hours and 20 minutes?
   Answer: 4,200 words This is a rate problem that asks you to find how much work gets done over a different time period. When you see questions about consistent rates of work, set up a proportion or find the rate per unit time. First, find Sarah's typing rate per minute. She types 450 words in 15 minutes, so her rate is $\frac{450 \text{ words}}{15 \text{ minutes}} = 30 \text{ words per minute}$. Next, convert the target time to minutes. 2 hours and 20 minutes equals $2 \times 60 + 20 = 140 \text{ minutes}$. Now multiply her rate by the total time: $30 \text{ words per minute} \times 140 \text{ minutes} = 4,200 \text{ words}$. This confirms answer A is correct. Let's examine why the other answers are wrong. Answer B (4,050 words) results from miscalculating the time conversion—you might get this if you incorrectly calculated 2 hours 20 minutes as 135 minutes instead of 140. Answer C (3,600 words) comes from using exactly 2 hours (120 minutes) and forgetting the additional 20 minutes: $30 \times 120 = 3,600$. Answer D (2,100 words) suggests a rate calculation error—perhaps dividing 4,200 by 2, indicating confusion about the time conversion or rate setup. For rate problems on the SSAT, always establish your rate clearly (words per minute, miles per hour, etc.), convert all time units to match your rate, then multiply. Double-check your time conversions—they're a common source of errors in these problems.
7. A machine fills bottles at a rate of 84 bottles every 7 minutes. How many bottles can it fill in 1 hour and 40 minutes?
   Answer: 1,200 Rate problems like this test your ability to work with proportional relationships and unit conversions. When you see a machine or process working at a constant rate, you're looking for a pattern you can scale up or down. First, find the rate per minute. If the machine fills 84 bottles in 7 minutes, it fills $84 \div 7 = 12$ bottles per minute. Next, convert the total time to minutes: 1 hour and 40 minutes equals $60 + 40 = 100$ minutes. Finally, multiply the rate by the time: $12 \times 100 = 1,200$ bottles. Looking at the wrong answers: Choice A (960) likely comes from miscalculating the rate as 96 bottles per 7 minutes instead of 84, then working with that incorrect rate. Choice B (1,080) suggests you might have calculated 90 minutes instead of 100 minutes for the total time, possibly forgetting that 1 hour and 40 minutes isn't 1 hour and 30 minutes. Choice D (1,320) could result from using the original 7-minute time period incorrectly in your calculations, perhaps multiplying 84 by some factor of the time conversion. The correct answer is C (1,200). For rate problems, always break them into three steps: find the unit rate (per minute, per hour, etc.), convert all time units to match, then multiply. Double-check your time conversions since mixing hours and minutes is where many students make careless errors on the SSAT.
8. A water faucet drips 240 drops in 8 minutes. At this rate, how many drops will fall in 3 hours and 20 minutes?
   Answer: 6,000 drops This is a classic rate problem that tests your ability to set up proportions and convert time units. When you see questions asking "at this rate," you're being asked to find a unit rate and then scale it up. First, find the rate of dripping. The faucet drips 240 drops in 8 minutes, so the rate is $\frac{240 \text{ drops}}{8 \text{ minutes}} = 30 \text{ drops per minute}$. Next, convert the target time to minutes. 3 hours and 20 minutes equals $(3 \times 60) + 20 = 180 + 20 = 200 \text{ minutes}$. Finally, multiply the rate by the time: $30 \text{ drops per minute} \times 200 \text{ minutes} = 6,000 \text{ drops}$. This confirms answer C is correct. Looking at the wrong answers: A) 4,800 drops results from miscalculating the time conversion—perhaps using 160 minutes instead of 200 minutes. B) 5,400 drops comes from using 180 minutes (forgetting to add the extra 20 minutes from "3 hours and 20 minutes"). D) 6,600 drops likely results from incorrectly calculating the rate as 33 drops per minute instead of 30. Strategy tip: In rate problems, always write out your unit rate clearly (drops per minute, miles per hour, etc.) and double-check your time conversions. Many students rush the time conversion step, but it's where most errors occur. Convert everything to the same units before multiplying.
9. Convert 7,200 seconds into hours and minutes. Which of the following represents the correct conversion?
   Answer: 2 hours and 0 minutes Time conversion problems require you to understand the relationships between different units. There are 60 seconds in a minute and 60 minutes in an hour, which means there are $60 \times 60 = 3,600$ seconds in one hour. To convert 7,200 seconds to hours, divide by 3,600: $7,200 ÷ 3,600 = 2$ hours exactly. Since this division results in a whole number with no remainder, there are 0 additional minutes. You can verify this: $2 \text{ hours} \times 3,600 \text{ seconds/hour} = 7,200 \text{ seconds}$. Looking at the wrong answers: Choice B (2 hours and 30 minutes) would equal $2 \times 3,600 + 30 \times 60 = 7,200 + 1,800 = 9,000$ seconds, which is too large. Choice C (1 hour and 50 minutes) equals $1 \times 3,600 + 50 \times 60 = 3,600 + 3,000 = 6,600$ seconds, which is too small. Choice D (1 hour and 60 minutes) contains an error in units—60 minutes equals 1 hour, so this should be written as 2 hours and 0 minutes, making it equivalent to choice A but incorrectly expressed. The correct answer is A: 2 hours and 0 minutes. Study tip: When converting time units, always remember that 3,600 seconds = 1 hour. For quick mental math, recognize that common time values like 1,800 seconds (30 minutes) or 900 seconds (15 minutes) can help you estimate and check your work.
10. A train travels at a constant speed of 75 miles per hour. At this rate, how many minutes will it take the train to travel 45 miles?
    Answer: 36 minutes This is a rate problem that asks you to find time when you know distance and speed. The key relationship to remember is: Distance = Rate × Time, which can be rearranged to find Time = Distance ÷ Rate. You're given that the train travels 45 miles at 75 miles per hour. Using the formula: Time = 45 miles ÷ 75 mph = 0.6 hours. Since the question asks for minutes, convert by multiplying by 60: 0.6 × 60 = 36 minutes. Let's examine why each answer choice might tempt you. Choice A (30 minutes) comes from incorrectly dividing 45 by 75 and getting 0.5, then converting to 30 minutes—but this calculation error misses that 45 ÷ 75 = 0.6, not 0.5. Choice C (40 minutes) might result from confusion with the conversion process or rounding errors in mental math. Choice D (45 minutes) is a classic trap that occurs when students mistakenly think the time equals the distance, forgetting to account for the speed entirely. The correct answer is B (36 minutes) because $\frac{45 \text{ miles}}{75 \text{ mph}} = 0.6 \text{ hours} = 36 \text{ minutes}$. Strategy tip: In rate problems, always identify what you're solving for first, then use the Distance = Rate × Time triangle. Cover the unknown variable to see the formula you need. Also, watch your units carefully—if the rate is in "per hour" but the answer wants minutes, don't forget that final conversion step.
11. A water tank is being filled at a rate of 8 gallons per minute. If the tank already contains 45 gallons and has a total capacity of 165 gallons, how many minutes will it take to fill the tank completely?
    Answer: 15 minutes When you encounter a tank-filling problem, you're working with a rate equation where you need to find how much more liquid is needed and divide by the filling rate. To solve this, first determine how much water still needs to be added. The tank's total capacity is 165 gallons, and it already contains 45 gallons, so you need: $165 - 45 = 120$ gallons more. Since water flows in at 8 gallons per minute, divide the remaining capacity by the rate: $\frac{120 \text{ gallons}}{8 \text{ gallons per minute}} = 15 \text{ minutes}$ Looking at the wrong answers: Choice B (20 minutes) likely comes from incorrectly calculating the remaining water needed—perhaps finding $165 - 45 = 120$ correctly but then dividing by 6 instead of 8. Choice C (12 minutes) might result from using the wrong capacity or rate in your calculation. Choice D (18 minutes) could come from computational errors in the division step. The correct answer is A: 15 minutes. Strategy tip: For rate problems, always identify three key pieces: the current amount, the target amount, and the rate of change. Then use the formula: Time = (Target - Current) ÷ Rate. Double-check that you're using the right units throughout—here, everything should be in gallons and minutes before you calculate.
12. A garden sprinkler uses 18 gallons of water in 30 minutes. How many gallons will it use in 2 hours and 45 minutes?
    Answer: 99 gallons This is a rate problem that asks you to find how much water is used over a different time period. When you see questions like this, you need to establish the rate first, then apply it to the new time frame. Start by finding the sprinkler's rate of water usage. If it uses 18 gallons in 30 minutes, then the rate is $\frac{18 \text{ gallons}}{30 \text{ minutes}} = 0.6 \text{ gallons per minute}$. Next, convert the target time to minutes: 2 hours and 45 minutes = 120 + 45 = 165 minutes. Now multiply the rate by the total time: $0.6 \times 165 = 99 \text{ gallons}$. Let's examine why the other answers are incorrect. Choice A (84 gallons) might result from incorrectly calculating the rate as 0.5 gallons per minute instead of 0.6, then multiplying by 168 minutes. Choice B (90 gallons) could come from using the correct rate but miscalculating the time conversion, perhaps using 150 minutes instead of 165. Choice C (96 gallons) might result from using 0.6 gallons per minute but calculating the time as 160 minutes instead of 165. The correct answer is D (99 gallons). For rate problems on the SSAT, always establish your rate first, convert all units to match (usually to the smaller unit like minutes), then multiply. Double-check your time conversions since mixing hours and minutes is a common source of error.
13. A swimming pool is being drained at a rate of 125 gallons every 5 minutes. At this rate, how long will it take to drain 2,000 gallons from the pool?
    Answer: 80 minutes This is a rate problem that tests your ability to work with proportional relationships. When you see questions about rates—whether it's draining pools, filling tanks, or other constant processes—you're looking for a consistent relationship between time and quantity. First, find the rate per minute. If 125 gallons drain every 5 minutes, then the rate is $125 ÷ 5 = 25$ gallons per minute. Now you can set up a proportion: if 25 gallons drain in 1 minute, how many minutes does it take to drain 2,000 gallons? Using the formula: $\text{time} = \frac{\text{total gallons}}{\text{rate per minute}} = \frac{2,000}{25} = 80$ minutes. Looking at the wrong answers: Choice B (75 minutes) would drain only 1,875 gallons at this rate—you might get this if you miscalculated the per-minute rate as roughly 26.7 gallons. Choice C (85 minutes) would drain 2,125 gallons, which is too much—this could result from rounding errors or arithmetic mistakes. Choice D (90 minutes) would drain 2,250 gallons, far exceeding what's needed—this might come from incorrectly using the original 5-minute interval in your calculations. The correct answer is A) 80 minutes. Strategy tip: For rate problems, always convert to a per-unit rate first (like gallons per minute), then use simple division. Double-check by multiplying your answer by the rate—you should get back to your target quantity. This verification step catches most calculation errors.
14. A factory worker can package 72 items in 45 minutes. Working at the same rate, how many complete items can the worker package in 2.5 hours?
    Answer: 240 items When you encounter a rate problem like this, you're dealing with proportional relationships. The key is finding the worker's rate and then scaling it to the new time period. First, find the worker's rate per hour. The worker packages 72 items in 45 minutes. Since 45 minutes equals $\frac{45}{60} = 0.75$ hours, the rate is $\frac{72 \text{ items}}{0.75 \text{ hours}} = 96$ items per hour. Now multiply this rate by the target time: $96 \text{ items/hour} \times 2.5 \text{ hours} = 240$ items. This confirms answer choice A is correct. Let's examine why the other answers are wrong. Choice B (216 items) likely comes from incorrectly calculating the hourly rate as 86.4 items per hour (perhaps from dividing 72 by 45 without converting to hours first). Choice C (180 items) might result from assuming the rate is 72 items per hour (forgetting that 45 minutes isn't a full hour). Choice D (200 items) could come from rounding errors or miscalculating the time conversion. The most common trap in rate problems is mixing up time units. Always convert everything to the same unit before calculating—in this case, converting 45 minutes to 0.75 hours was crucial. When you see rate problems on the SSAT, immediately identify what units you're working with and convert them to match before setting up your proportion.
15. A recipe that serves 8 people requires 2.5 cups of rice. How many cups of rice are needed to serve 20 people using the same recipe?
    Answer: 6.25 cups This is a proportional reasoning problem where you need to scale a recipe up from one serving size to another. When you see questions about recipes, rates, or any situation where quantities change together in a fixed ratio, think about setting up a proportion. Start by identifying what you know: 2.5 cups of rice serves 8 people. You need to find how much rice serves 20 people. Set up a proportion comparing cups of rice to number of people: $\frac{2.5 \text{ cups}}{8 \text{ people}} = \frac{x \text{ cups}}{20 \text{ people}}$ Cross multiply: $2.5 \times 20 = 8 \times x$, which gives you $50 = 8x$. Solving for x: $x = \frac{50}{8} = 6.25$ cups. You can also think of this as finding the scaling factor: 20 ÷ 8 = 2.5, so you need 2.5 times the original recipe. Therefore: 2.5 cups × 2.5 = 6.25 cups. Looking at the wrong answers: B) 6 cups likely comes from rounding 6.25 down or making an arithmetic error. C) 5.5 cups might result from incorrectly setting up the proportion or miscalculating the scaling factor. D) 7 cups could come from rough estimation or computational mistakes in the cross multiplication. The correct answer is A) 6.25 cups. For proportion problems, always double-check by asking: "Does this make sense?" Since you're serving more people (20 vs 8), you definitely need more rice than the original 2.5 cups, and 6.25 is reasonable for that increase.
16. A jogger runs 3.6 kilometers in 18 minutes. At this pace, how many meters will the jogger cover in 25 minutes?
    Answer: 5,000 meters This is a unit rate and proportion problem that tests your ability to work with different units of measurement and time intervals. When you see questions asking "at this pace" or "at this rate," you need to find the rate per unit of time first. Start by finding the jogger's rate per minute. The jogger runs 3.6 kilometers in 18 minutes, so the rate is $\frac{3.6 \text{ km}}{18 \text{ min}} = 0.2 \text{ km per minute}$. Now you can find the distance covered in 25 minutes: $0.2 \times 25 = 5 \text{ km}$. Since the answer choices are in meters, convert: $5 \text{ km} = 5,000 \text{ meters}$. Answer choice (A) 4,500 meters represents a calculation error where you might have used 22.5 minutes instead of 25 minutes, or made an error in the rate calculation. Answer choice (B) 4,800 meters could result from incorrectly calculating the rate as 0.192 km per minute instead of 0.2. Answer choice (D) 5,200 meters might come from rounding errors or using an incorrect rate of 0.208 km per minute. The correct answer is (C) 5,000 meters. For rate problems like this, always set up your calculation in clear steps: find the unit rate first, multiply by the new time period, then check your units carefully. Many students make errors by rushing through unit conversions or mixing up kilometers and meters in their calculations.
17. A photocopier can make 420 copies in 14 minutes. At this rate, how many copies can it make in 50 minutes?
    Answer: 1,500 copies This is a rate problem where you need to find how many copies can be made at a consistent rate over a different time period. When you see "at this rate" in a problem, you're looking at proportional relationships. First, find the photocopier's rate per minute. If it makes 420 copies in 14 minutes, divide: $420 ÷ 14 = 30$ copies per minute. Now multiply this rate by the new time period: $30 \times 50 = 1,500$ copies in 50 minutes. You can also solve this using proportions: $\frac{420 \text{ copies}}{14 \text{ minutes}} = \frac{x \text{ copies}}{50 \text{ minutes}}$. Cross-multiply: $420 \times 50 = 14x$, so $21,000 = 14x$, giving you $x = 1,500$. Looking at the wrong answers: Choice A (1,200) might result from incorrectly calculating the per-minute rate or making an arithmetic error. Choice B (1,400) could come from confusing the given numbers or miscalculating $30 \times 50$. Choice D (1,680) might occur if you mistakenly used 420 copies as a base and applied an incorrect multiplier. For rate problems on the SSAT, always identify what's being measured per unit of time first, then scale up or down accordingly. Double-check your arithmetic—especially multiplication—since these problems often involve larger numbers where calculation errors are common.
18. A recipe calls for 3 cups of flour to make 24 cookies. How many cups of flour are needed to make 40 cookies?
    Answer: 5 cups of flour This is a proportion problem that tests your ability to scale recipes up or down. When you see questions involving recipes, rates, or "per unit" relationships, you're dealing with proportional reasoning. The key is setting up a proportion that compares the relationship between flour and cookies. You know that 3 cups of flour makes 24 cookies, and you need to find how much flour makes 40 cookies. Set this up as: $\frac{3 \text{ cups}}{24 \text{ cookies}} = \frac{x \text{ cups}}{40 \text{ cookies}}$ Cross multiply to solve: $3 \times 40 = 24 \times x$, which gives you $120 = 24x$. Dividing both sides by 24: $x = 5$ cups of flour. Looking at the wrong answers: Choice A (4 cups) might come from incorrectly thinking you need to add just 1 more cup since you're making more cookies, but this ignores the actual proportional relationship. Choice C (4.5 cups) could result from setting up the proportion incorrectly or making an arithmetic error during cross multiplication. Choice D (6 cups) might come from doubling the original amount since 40 is somewhat close to double 24, but this oversimplifies the relationship. The correct answer is B (5 cups of flour). Strategy tip: For proportion problems, always set up your ratios consistently—keep the same units in the same position (flour on top, cookies on bottom, or vice versa). Double-check by seeing if your answer makes sense: since 40 cookies is less than double 24 cookies, you'd expect less than double the flour (less than 6 cups).
19. A carpenter can cut 45 boards in 1 hour and 15 minutes. Working at the same pace, how many boards can be cut in 3 hours and 20 minutes?
    Answer: 120 When you encounter rate problems like this, you need to establish a consistent rate and then apply it to the new time period. The key is converting all times to the same units and setting up a proportion. First, convert the given time to minutes: 1 hour and 15 minutes = 75 minutes. So the carpenter cuts 45 boards in 75 minutes. To find the rate per minute: $\frac{45 \text{ boards}}{75 \text{ minutes}} = \frac{3}{5} = 0.6$ boards per minute. Next, convert the target time: 3 hours and 20 minutes = 200 minutes. At a rate of 0.6 boards per minute: $200 \times 0.6 = 120$ boards. Looking at the wrong answers: Choice A (90) represents a common error where students might think that since 3 hours 20 minutes is roughly 2.67 times the original 1 hour 15 minutes, they incorrectly calculate $45 \times 2 = 90$. Choice B (108) could result from miscalculating the time conversion or rate. Choice D (135) might come from incorrectly treating 3 hours 20 minutes as exactly 3 times 1 hour 15 minutes and calculating $45 \times 3 = 135$. The correct answer is C: 120 boards. Study tip: For rate problems, always convert times to the same units (usually minutes) before calculating. Set up your rate as a fraction, then multiply by the new time period. Double-check your time conversions—this is where many students make careless errors.
20. A conveyor belt moves 480 feet in 12 minutes. How many yards will the belt move in 45 minutes?
    Answer: 600 yards This problem tests your ability to work with rates and unit conversions—two skills that often appear together on the SSAT. When you see a question involving different units and time periods, break it into steps: find the rate, convert units if needed, then apply the rate to the new time period. First, find the belt's speed. The belt moves 480 feet in 12 minutes, so its rate is $\frac{480 \text{ feet}}{12 \text{ minutes}} = 40 \text{ feet per minute}$. Next, calculate how far it moves in 45 minutes: $40 \text{ feet/minute} \times 45 \text{ minutes} = 1,800 \text{ feet}$. Finally, convert feet to yards. Since 1 yard = 3 feet, divide by 3: $\frac{1,800 \text{ feet}}{3} = 600 \text{ yards}$. This confirms answer C is correct. Looking at the wrong answers: A) 480 yards likely comes from confusing the original 480 feet measurement with the final answer, forgetting both the time change and unit conversion. B) 540 yards might result from miscalculating the rate or making an error in the time multiplication. D) 660 yards could come from calculation errors or incorrect unit conversion. Strategy tip: For rate problems with unit conversions, always work systematically: calculate the rate first, apply it to the new situation, then handle unit conversions at the end. Don't try to convert units and change time periods simultaneously—you're more likely to make errors that way.

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