At 8:00 am, Sarah began working on a project by herself. After completing a 10-hour shift, which included a 1-hour break for lunch, she managed to finish part of her work. The following day, she returns at the same time, but this time she is joined by her coworker, Tom, who assists her in completing the project by 4:00 pm. Since they finished the task before the end of their shift, neither took a lunch break. If Tom can finish the entire project in 12 hours, how long would it take Sarah to finish the project if she worked alone?

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Official Explanation

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At the conclusion of the project, Sarah has worked for 9 + 8 = 17 hours, while Tom has worked for 0 + 8 = 8 hours. The problem states that Tom can complete 100% of the work in 12 hours. The percentage of work completed by Tom in 8 hours is given by

\frac{100 }{ 12 * 8} = \frac{100 * 8 }{ 12 * 10} = \frac{200}{3}

. The percentage of work…

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What this question tests

What it tests

Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.

Common trap

Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.