SAT Math Multiple Choice Question 234: Answer and Explanation

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Question: 234

9.

Rick, Shane, and Darryl work at a widget factory. The table above shows the number of hours they each spent at the factory on a given day, the number of widgets they produced, and the number of 15-minute breaks they took while they were at the factory. Each man works at a constant rate.

Rick and Shane are each assigned an equal number of widgets. Neither will take breaks in order to complete this assignment as quickly as possible. Rick offers to do a certain percentage of Shane's assignment so that they both finish at the same time. What percentage of Shane's original assignment does Rick do?

  • A. 12.50%
  • B. 14.30%
  • C. 16.70%
  • D. 25%

Correct Answer: B

Explanation:

B First, solve for Rick's hourly rate and Shane's hourly rate. Since Work = Rate × Time, Rick produces 8 widgets per hour (28 widgets ÷ 3.5 hours without breaks) and Shane produces 27 ÷ 3.5 = 6 widgets per hour. Now plug in. Since you know they have a combined rate of 14 widgets per hour, choose a total amount that is divisible by 14. Let's say they were each assigned 14. This means that the total produced is 28, and at a total rate of 14 per hour. Therefore, it takes them 2 hours to finish. During this time Rick would produce 16 widgets and Shane would produce 12 widgets. Therefore, Rick must have done 2 of Shane's originally assigned 14 widgets, which is 14.3% of 14. This matches (B).

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