SSAT Middle Level Quiz: Work And Rate Problems

5 questions · exam conditions

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Work And Rate ProblemsQuestion 1 of 5

Two garden hoses can fill a swimming pool. Hose A fills at 15 gallons per minute, and Hose B fills at 20 gallons per minute. If the pool holds 1350 gallons and Hose A runs for 20 minutes before Hose B is turned on, how many additional minutes will it take with both hoses running to fill the pool?

28

minutes

30

minutes

32

minutes

34

minutes

36

minutes

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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Work And Rate Problems

Practice Work And Rate Problems in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Work And Rate Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

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.

All questions

Question 1

$28$ minutes
$30$ minutes (correct answer)
$32$ minutes
$34$ minutes
$36$ minutes

Explanation: When you encounter a multi-step rate problem like this, break it down into phases and track what happens in each one. First, calculate how much water Hose A adds during its solo 20 minutes:

15 \text{ gallons/minute} \times 20 \text{ minutes} = 300 \text{ gallons}

. This leaves

1350 - 300 = 1050 \text{ gallons}

still needed. Next, determine the combined rate when both hoses run together:

15 + 20 = 35 \text{ gallons per minute}

. To find how long it takes to fill the remaining 1050 gallons at this combined rate:

\frac{1050 \text{ gallons}}{35 \text{ gallons/minute}} = 30 \text{ minutes}

. This confirms answer B. Now let's see where the wrong answers come from. Choice A (28 minutes) likely results from a calculation error, perhaps incorrectly computing

\frac{1050}{35}

. Choice C (32 minutes) might come from using the wrong remaining volume or making an arithmetic mistake in the division. Choice D (34 minutes) could result from forgetting to add the rates together and instead using just one hose's rate for the second phase. The key strategy for rate problems is to organize your work in clear steps: identify what happens in each time period, calculate any intermediate amounts, then solve for the unknown time using the formula

\text{time} = \frac{\text{amount}}{\text{rate}}

. Always double-check that your rates match the scenario—individual rates for solo work, combined rates when working together.

Question 2

A swimming pool is being filled and drained simultaneously. The inlet pipe fills the pool at 40 gallons per minute, while the drain removes water at 25 gallons per minute. If the pool starts with 200 gallons and has a capacity of 800 gallons, how long will it take to fill the pool completely?

$35$ minutes
$40$ minutes (correct answer)
$45$ minutes
$50$ minutes
$55$ minutes

Explanation: When you encounter problems involving simultaneous filling and draining, think about the net rate of change. You need to find how much water is actually being added to the pool each minute after accounting for both the inflow and outflow. The inlet adds 40 gallons per minute while the drain removes 25 gallons per minute, giving you a net rate of

40 - 25 = 15

gallons per minute. This means the pool gains 15 gallons every minute. Since the pool starts with 200 gallons and needs to reach 800 gallons, it needs

800 - 200 = 600

more gallons. At a net rate of 15 gallons per minute, this will take

600 \div 15 = 40

minutes. Looking at the wrong answers: Choice A (35 minutes) likely comes from incorrectly calculating the gallons needed or making an arithmetic error. Choice C (45 minutes) might result from using the wrong net rate, perhaps calculating

40 - 25 = 13.33

through sloppy math. Choice D (50 minutes) could come from dividing 600 by 12 instead of 15, suggesting confusion about the net rate calculation. The correct answer is B: 40 minutes. Study tip: For rate problems involving opposing forces (filling vs. draining, traveling with vs. against wind, etc.), always identify the net effect first. Subtract the opposing rate from the working rate, then use this net rate for your time calculations. This approach prevents the common mistake of using individual rates instead of the combined effect.

Question 3

A water tank can be filled by two pipes. Pipe A fills the tank in 15 hours when working alone. When both pipes work together, they fill the tank in 6 hours. If Pipe B works alone for 4 hours and then both pipes work together, how much additional time is needed to fill the tank completely?

3 hours
3½ hours (correct answer)
4 hours
4½ hours
5 hours

Explanation: When you encounter work rate problems involving multiple workers or pipes, think in terms of rates of work completion. Each pipe has a rate measured in "fraction of tank filled per hour." Pipe A fills the tank in 15 hours, so its rate is

\frac{1}{15}

tank per hour. When both pipes work together, they complete the job in 6 hours, giving a combined rate of

\frac{1}{6}

tank per hour. To find Pipe B's rate: Combined rate = Pipe A's rate + Pipe B's rate, so

\frac{1}{6} = \frac{1}{15} + \frac{1}{B}

. Solving:

\frac{1}{B} = \frac{1}{6} - \frac{1}{15} = \frac{5-2}{30} = \frac{1}{10}

. Therefore, Pipe B fills the tank in 10 hours working alone. Now for the actual problem: Pipe B works alone for 4 hours, filling

4 \times \frac{1}{10} = \frac{4}{10} = \frac{2}{5}

of the tank. This leaves

1 - \frac{2}{5} = \frac{3}{5}

of the tank remaining. When both pipes work together at their combined rate of

\frac{1}{6}

tank per hour, the time needed to fill the remaining

\frac{3}{5}

is:

\frac{3/5}{1/6} = \frac{3}{5} \times 6 = 3.6

hours = 3½ hours. Choice A (3 hours) incorrectly assumes the remaining work is

\frac{1}{2}

of the tank. Choice C (4 hours) mistakes Pipe B's solo time for the combined working time. Choice D (4½ hours) likely results from calculation errors in finding the combined rate. Remember: always convert rates to fractions first, then work systematically through each phase of the problem.

Question 4

A warehouse uses two conveyor belts to move packages. Belt A moves 45 packages per hour, and Belt B moves 36 packages per hour. If Belt A breaks down after moving packages for 3 hours and Belt B continues alone to move a total of 500 packages, how many additional hours must Belt B operate?

9 hours
10 hours
11 hours (correct answer)
12 hours
13 hours

Explanation: When you encounter multi-step work rate problems, break them down into phases and track what each worker accomplishes in each phase. First, calculate what Belt A accomplished before breaking down. At 45 packages per hour for 3 hours, Belt A moved

45 \times 3 = 135

packages. Since the total goal is 500 packages, Belt B must handle the remaining work:

500 - 135 = 365

packages. Now determine how long Belt B needs to move these 365 packages. At Belt B's rate of 36 packages per hour:

\frac{365}{36} = 10.14

hours. Since we need complete hours and Belt B must finish all packages, this rounds up to approximately 11 hours. Let's verify: Belt B moving for 11 hours produces

36 \times 11 = 396

packages, which exceeds the required 365 packages. Answer choice A (9 hours) gives Belt B only

36 \times 9 = 324

packages, falling short of the needed 365. Answer choice B (10 hours) produces

36 \times 10 = 360

packages, still 5 packages short. Answer choice D (12 hours) would work but represents more time than necessary, making it inefficient. Answer choice C (11 hours) is correct because it's the minimum whole number of hours needed for Belt B to complete the remaining work. Study tip: In work rate problems with breakdowns or interruptions, always calculate the remaining work after the interruption, then determine the time needed based on the continuing worker's rate. Round up when dealing with minimum time requirements.

Question 5

A bakery has two ovens. Oven 1 can bake 24 loaves per hour, and Oven 2 can bake 18 loaves per hour. If they need to bake 300 loaves and Oven 1 operates for 6 hours while Oven 2 operates for the entire time needed, how many total hours must Oven 2 operate?

8 hours
9 hours (correct answer)
10 hours
11 hours
12 hours

Explanation: When you encounter work rate problems involving multiple machines or workers operating for different time periods, you need to track each contributor's output separately and then combine them to reach the total requirement. Let's call the total time Oven 2 operates

t

hours. Since Oven 1 operates for only 6 hours at 24 loaves per hour, it produces

6 \times 24 = 144

loaves. Oven 2 operates for the full

t

hours at 18 loaves per hour, producing

18t

loaves. Together, they must bake 300 loaves total. Setting up the equation:

144 + 18t = 300

Solving for

t

18t = 300 - 144 = 156

, so

t = 156 ÷ 18 = 8.67

hours, which rounds to approximately 9 hours when we verify:

144 + (18 \times 9) = 144 + 162 = 306

loaves (slightly over 300, which is acceptable since we can't operate partial hours). Choice A (8 hours) falls short:

144 + (18 \times 8) = 288

loaves, which is 12 loaves under the requirement. Choice C (10 hours) produces

144 + 180 = 324

loaves, significantly more than needed. Choice D (11 hours) produces

144 + 198 = 342

loaves, which is excessive. Therefore, B is correct. Strategy tip: In work rate problems with different operating times, always set up your equation by adding each worker's individual contribution (rate × time = output) and setting the sum equal to the total requirement. Double-check your answer by substituting back into the original scenario.