SAT Math Quiz: Rates

What this quiz covers

This quiz focuses on Rates, giving you a quick way to practice the rules, question types, and explanations that matter most for SAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $90\text{ min}$
2. $60\text{ min}$
3. $24.3\text{ min}$
4. $75\text{ min}$ (correct answer)

Explanation: Draining at a constant rate makes this time = volume divided by rate, so compute 1,350 gallons divided by 18 gallons per minute. Since 18 times 75 equals 1,350, the answer is 75 minutes, and the gallons cancel to leave minutes. The 90-minute figure would drain 18 times 90, or 1,620 gallons, more water than the pool holds, so it runs too long. The 60-minute figure removes only 18 times 60, or 1,080 gallons, leaving 270 gallons still in the pool. The 24.3-minute figure comes from multiplying instead of dividing, essentially 18 times 1.35, which is the wrong operation; a hose moving just 18 gallons a minute cannot empty over a thousand gallons in under half an hour. Setting the problem up so the gallon units cancel keeps you from inverting the division.

Question 2

1. $31.20
2. $3.12
3. $19.50 (correct answer)
4. $10.30

Explanation: At a fixed price per pound, total cost equals price times pounds, so 7.80 for each of 2.5 pounds gives 19.50 dollars. Splitting it up confirms this: 2 pounds cost 15.60, half a pound costs 3.90, and 15.60 plus 3.90 is 19.50. The 3.12 figure comes from dividing 7.80 by 2.5, the reverse operation, which answers a different question entirely. The 10.30 figure comes from adding 7.80 and 2.50, combining dollars with pounds, quantities that cannot be added meaningfully. The 31.20 figure equals 7.80 times 4, so it multiplies by the wrong quantity; it should also look too large, since 2.5 pounds must cost between two and three times the one-pound price, putting the answer somewhere between 15.60 and 23.40.

Question 3

1. $8\text{ s/box}$
2. $80\text{ s/box}$
3. $7.5\text{ s/box}$ (correct answer)
4. $0.125\text{ s/box}$

Explanation: This is a unit-rate question, and the answer must be in seconds per box. Convert the time first: 6 minutes = 360 seconds. Then divide by the number of boxes: 360/48 = 7.5, so 7.5 seconds per box is correct. The answer 8 s/box comes from dividing 48 by 6 without converting anything; 8 is really the number of boxes per minute, so the units are backwards. The answer 0.125 s/box is 6/48, which is the time per box in minutes rather than seconds; multiplying it by 60 produces 7.5. The answer 80 s/box is off by a factor of about ten from any correct division, and it fails a quick sanity check: at 80 seconds per box the machine would finish only about 4.5 boxes in 6 minutes, not 48.

Question 4

1. $24\text{ pages}$
2. $210\text{ pages}$
3. $240\text{ pages}$ (correct answer)
4. $1{,}440\text{ pages}$

Explanation: We need to find how many pages print in 8 minutes when 180 pages print in 6 minutes. The rate is 180 pages ÷ 6 minutes = 30 pages per minute. For 8 minutes: 30 pages/minute × 8 minutes = 240 pages. Watch out for dividing when you should multiply - if the rate is pages per minute and you have minutes, multiply to get pages. The units (pages/minute × minutes = pages) confirm the operation.

Question 5

1. $0.017\text{ h/km}$
2. $60\text{ km/h}$ (correct answer)
3. $1.5\text{ km/h}$
4. $135\text{ km/h}$

Explanation: We need the car's speed in kilometers per hour when it travels 90 km in 1.5 hours. Speed = distance ÷ time = 90 km ÷ 1.5 hours = 60 km/h. This is a straightforward rate calculation where the units work out to km/h as required. Avoid the reciprocal error of calculating 1.5/90 = 0.017, which would give hours per kilometer instead of the requested kilometers per hour.

Question 6

1. $25\text{ L}$
2. $126\text{ L}$ (correct answer)
3. $2.57\text{ L}$
4. $324\text{ L}$

Explanation: We need total liters drained in 7 minutes at 18 liters per minute. Using total = rate × time: 18 liters/minute × 7 minutes = 126 liters. The multiplication is confirmed by unit analysis: liters/minute × minutes = liters. A common error is dividing 18 by 7, which would give a rate (liters per minute) rather than a total amount. When you have a rate and a time, multiply to get the total.

Question 7

1. $12.5\text{ min}$ (correct answer)
2. $138\text{ min}$
3. $1{,}800\text{ min}$
4. $0.08\text{ min}$

Explanation: We need to find the time to add 150 gallons at a rate of 12 gallons per minute. Using time = total ÷ rate: 150 gallons ÷ 12 gallons/minute = 12.5 minutes. The key is recognizing that when you divide gallons by gallons per minute, the gallons cancel and you're left with minutes. A common error is multiplying 150 × 12, which would give gallons squared per minute - nonsensical units.

Question 8

1. 60 bolts
2. 630 bolts
3. 900 bolts (correct answer)
4. 840 bolts

Explanation: We need to find how many bolts are produced in 15 minutes at a constant rate. First, calculate the rate: 420 bolts ÷ 7 minutes = 60 bolts per minute. In 15 minutes: 60 bolts/min × 15 min = 900 bolts. The key is finding the rate first, then multiplying by the new time. Common errors include dividing by 15 or treating 420 as the rate per minute. Always identify what the given numbers represent before calculating.

Question 9

1. $0.071$ items/min
2. $12$ items/min
3. $14$ items/min (correct answer)
4. $504$ items/min

Explanation: We need to find the scanning rate in items per minute. Calculate: 84 items ÷ 6 minutes = 14 items per minute. This tells us the cashier scans 14 items every minute at this constant rate. A common mistake is computing 6 ÷ 84 = 0.071, which gives minutes per item instead of items per minute. Always check that your final units match what the question asks for - here we want items/minute, not minutes/item.

Question 10

1. $19.4\text{ min/word}$
2. $50\text{ words/min}$
3. $60\text{ words/min}$ (correct answer)
4. $90\text{ words/min}$

Explanation: Words per minute means words divided by minutes, so divide 1,080 words by 18 minutes to get 60 words per minute. The check works: 60 words per minute for 18 minutes yields 1,080 words. The answer given as 19.4 min/word is wrong in both value and units, since minutes per word would be 18 divided by 1,080, roughly 0.017, and the question asks for words per minute. The 50 words per minute figure would produce only 900 words in 18 minutes, well short of 1,080. The 90 words per minute figure would produce 1,620 words, far more than the student actually typed; it comes from dividing 1,080 by 12 rather than by 18. Whenever you compute a rate, multiply it back by the time to confirm you recover the original total.

Question 11

1. $11.70
2. $20.80 (correct answer)
3. $31.20
4. $5.20

Explanation: We need to find the cost of 4 pounds of almonds when 1.5 pounds cost $7.80. The rate is $7.80 per 1.5 pounds, which equals $5.20 per pound ($7.80 ÷ 1.5). For 4 pounds, multiply: $5.20/pound × 4 pounds = $20.80. A common mistake is multiplying $7.80 by 4 without first finding the per-pound rate. Always convert to unit rate (dollars per pound) before scaling up.

Question 12

1. Cyclist A, $15\text{ mph}$ (correct answer)
2. Cyclist A, $21.6\text{ mph}$
3. Cyclist B, $12.5\text{ mph}$
4. Cyclist B, $0.08\text{ hr/mi}$

Explanation: We need to compare speeds and identify the faster cyclist in miles per hour. Cyclist A: 18 miles ÷ 1.2 hours = 15 mph. Cyclist B: 25 miles ÷ 2 hours = 12.5 mph. Cyclist A is faster at 15 mph. Be careful not to compare total distances (25 > 18) without accounting for time differences. The correct comparison requires calculating rate as distance per unit time.

Question 13

1. 1,760 (correct answer)
2. 5,280
3. 105,600
4. 1,760,000

Explanation: 1. Convert miles to yards: 60 \text{ miles/hr} \times 1,760 \text{ yards/mile} \= 105,600 \text{ yards/hr}. 2. Convert hours to minutes: 105,600 \text{ yards/hr} \div 60 \text{ min/hr} \= 1,760 \text{ yards/min}. SAT Strategy: Think Logically For those paying attention to the numbers chosen in this problem this can be a quick mental math problem. 60 miles per hour is the same as one mile per minute. And since you're asked for yards per minute, and given that 1 mile = 1,760 yards, you can do that conversion without even needing a calculator or pencil.

Question 14

1. 21.3 yd$^3$
2. 10.7 yd$^3$
3. 25.6 yd$^3$
4. 24.0 yd$^3$ (correct answer)

Explanation: We need to find cubic yards of mulch spread in 7.5 hours at a rate of 3.2 cubic yards per hour. This is a direct multiplication: 3.2 yd³/hour × 7.5 hours = 24.0 cubic yards. To calculate: 3.2 × 7.5 = 3.2 × 7 + 3.2 × 0.5 = 22.4 + 1.6 = 24.0. Common errors include decimal multiplication mistakes or forgetting to include units. When given a rate and time, multiply to find the total quantity.

Question 15

1. 12
2. 15 (correct answer)
3. 13
4. 1.15

Explanation: Percent increase is (92 - 80)/80 * 100 = 15. 12 is the absolute difference, 13 uses the new price as the base, and 1.15 is the multiplier, not the percent.

Question 16

1. 15,840
2. 15,000
3. 14,080 (correct answer)
4. 13,840

Explanation: This is a classic unit conversion / dimensional analysis problem, where you can stack the units in a multiplication problem to eliminate the units like you would reduce fractions and end up with the units (feet) you need. You have the following inputs: 1 mile = 5,280 feet Rate = 4 miles / 1 hour Time = 40 minutes And you know that 1 hour = 60 minutes. so to get from 4 miles/hour to "feet" just line up your units so that they cancel: \frac{4 miles}{1 hour} \times \frac{5280 feet}{1 mile} \times \frac{1 hour}{60 minutes} \times 40 minutes \= 14,080 And since all the units cancel except for feet in the numerator, you can be sure that your answer is in the right units: 14,080 feet.

Question 17

1. 80 kilometers/hour (correct answer)
2. 70 kilometers/hour
3. 75 kilometers/hour
4. 72 kilometers/hour

Explanation: This question asks for the train's speed in kilometers per hour. Speed is a rate expressing distance traveled per unit of time. Using the rate formula: speed = distance ÷ time, we calculate 360 kilometers ÷ 4.5 hours = 80 kilometers per hour. The units cancel correctly: km/hours = km per hour. Students might make arithmetic errors with the decimal division or confuse the order of division. When finding speed, always divide the total distance by the total time to get the rate per hour.

Question 18

1. 5 hours
2. 2 hours
3. 3 hours
4. 4 hours (correct answer)

Explanation: This question asks how long the task will take with a 50% speed increase. First, find the original work rate: 1 task ÷ 6 hours = $1/6$ task per hour. With a 50% speed increase, the new rate becomes 1.5 × ($1/6$) = $1.5/6$ = $1/4$ task per hour. Using time = work ÷ rate: 1 task ÷ ($1/4$ task per hour) = 4 hours. The key insight is that increasing speed by 50% means multiplying the rate by 1.5, not reducing time by 50%. Remember that when work rates increase, completion times decrease proportionally.

Question 19

1. 1.67 hours
2. 2.0 hours
3. 2.5 hours (correct answer)
4. 3.0 hours

Explanation: We need to find how long it takes to ride 30 miles at a constant speed. First, calculate the cyclist's speed: 18 miles ÷ 1.5 hours = 12 miles per hour. To find the time for 30 miles, divide distance by speed: 30 miles ÷ 12 miles/hour = 2.5 hours. The key is using distance/speed = time, not mixing up the rate formula. A common error is using hours per mile (1.5/18) instead of miles per hour. When dealing with rates, always check your units match what you're solving for.

Question 20

1. $630 (correct answer)
2. $560
3. $35
4. $756

Explanation: We need to find earnings for 18 hours when the contractor earns $420 for 12 hours. The hourly rate is $420 ÷ 12 hours = $35 per hour. For 18 hours: $35/hour × 18 hours = $630. This maintains the same hourly rate for the longer work period. A common error is trying to use a proportion without finding the hourly rate first, which can lead to calculation mistakes. For pay rate problems, always find the per-hour rate as an intermediate step.