Bunuel wrote:
Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?
A. 5
B. 20
C. 30
D. 60
E. 120
Standard
\(rt = W\) works well here
Sam's rate = \(\frac{1}{3}\)
Mark's rate = \(\frac{1}{12}\)
1) Rate at which they work together:
\((\frac{1}{3}\) + \(\frac{1}{12})\) = \(\frac{15}{36}\) = \(\frac{5}{12}\) is combined rate
2) In two hours, they finish how much work?
\(W = rt\)W = \((\frac{5}{12} * 2) = \frac{5}{6}\) of work is finished
3) Time, in minutes, for Sam to finish remaining work alone? (Work/Sam's rate) = Sam's time. Then convert hours to minutes.
\(\frac{1}{6}\) of work remains
\(\frac{\frac{1}{6}}{\frac{1}{3}} =(\frac{1}{6} * 3) =\frac{1}{2}hr\)
\(\frac{1}{2}hr\) = \(30\) minutes*
Answer C
*
\(\frac{1}{2}hr\) = 30 minutes is easy. With harder numbers, just multiply any fraction of an hour by 60 to get minutes. Example:
\((\frac{17}{12}hr)\) * (60) = 85 minutes _________________
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