Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?
A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2
Less than a minute to solve: Break the problem into two stages. Use RT = W
Rates in jobs per hour:
Sam's rate (use in Stage 1): \(\frac{1}{4}\)
Peter's rate: \(\frac{1}{3}\)
Combined rate (use in Stage 2):
\((\frac{1}{4}+ \frac{1}{3})=\frac{7}{12}\)
Convert Sam's time working alone:
30 minutes = \(\frac{1}{2}\) hour*
Stage 1: Sam works aloneTotal work is 1 (job)
How much work did Sam finish in 30 minutes?
R*T = W
R = \(\frac{1}{4}\)
T = \(\frac{1}{2}\) hour
\((\frac{1}{4}*\frac{1}{2})=\frac{1}{8}\)
of work
is finished by Sam
How much work remains?
(Total W - Sam's W)
\((1-\frac{1}{8})=\frac{7}{8}\) of work remains for both to finish
Stage 2: they work togetherHow many hours will they need to finish the rest of the work?
R*T = W
R (
combined, above): \(\frac{7}{12}\)
T = ?
W = \(\frac{7}{8}\)
\(\frac{7}{12}*T=\frac{7}{8}\)
\(T=(\frac{7}{8} * \frac{12}{7}) = \frac{12}{8}=\frac{3}{2}\)
Answer A*\((30.mins*\frac{1hr}{60.mins})=\frac{30hr}{60}=\frac{1}{2}\) hour
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