SAT Math Multiple Choice Practice Question 386: Answer and Explanation

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Question: 386

12. Stephanie can clean a pool in 1 hour, and Mark can clean the same pool in 1.5 hours. If the rate at which they work together is the sum of their rates working separately, how many minutes should they need to clean the pool if they work together? (1 hour = 60 minutes)

A. 24 minutes
B. 36 minutes
C. 60 minutes
D. 72 minutes
E. 100 minutes

Correct Answer: B


B A little common sense should tell you that they will not need a full hour to clean the pool, because Stephanie can clean it in an hour all by herself, but Mark is helping. Therefore, you should eliminate choices (C), (D), and (E) right away. You might also notice that it can't take less than 30 minutes, because that is how long it would take if they both cleaned one pool per hour (so that the two working together could clean it in half the time), but Mark is slower, so they can't clean it quite that fast. This eliminates choice (A) and leaves (B) as the only possibility.

But you should know how to solve this problem if it were not a multiple-choice question, as well:

Stephanie's rate for cleaning the pool is one pool per hour. Mark's rate for cleaning the pool is one pool ÷ 1.5 hours = pools per hour. Combined, they can clean pools per hour. Set up a rate equation using this rate to determine how much time it would take to clean one pool:

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