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Pat takes 4 hours to complete a work, Quinn takes 6 hours and Rob ta
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25 Dec 2024, 12:36
25 Dec 2024, 12:36
Expert Reply
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Question Stats:
20% (01:22) correct
80% (02:17) wrong based on 5 sessions
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Pat takes 4 hours to complete a work, Quinn takes 6 hours and Rob takes 8 hours to complete the same amount of work when they work alone. If the three people work together to complete the same work, approximately what percentage of the total work is done by Pat?
A. 42%
B. 46%
C. 50%
D. 54%
E. 60%
A. 42%
B. 46%
C. 50%
D. 54%
E. 60%
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Pat takes 4 hours to complete a work, Quinn takes 6 hours and Rob ta
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02 Feb 2025, 07:41
02 Feb 2025, 07:41
Expert Reply
OE
We know that Pat, Quinn \& Rob take 4 hours, 6 hours \& 8 hours respectively to complete the same amount of work individually, so their combined speed is $\(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}=\frac{6+4+3}{24}=\frac{13}{24}\)$
Finally the percentage of work done by Pat when all three work together is $\(\frac{ Speed of Pat }{ Combined speed of Pat, Quinn \& Rob } \times 100=\frac{\frac{1 }{ 4}}{\frac{13 }{ 24}} \times 100=\frac{6}{13} \times 100 \sim 46 \%\)$
Hence the answer is (B).
We know that Pat, Quinn \& Rob take 4 hours, 6 hours \& 8 hours respectively to complete the same amount of work individually, so their combined speed is $\(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}=\frac{6+4+3}{24}=\frac{13}{24}\)$
Finally the percentage of work done by Pat when all three work together is $\(\frac{ Speed of Pat }{ Combined speed of Pat, Quinn \& Rob } \times 100=\frac{\frac{1 }{ 4}}{\frac{13 }{ 24}} \times 100=\frac{6}{13} \times 100 \sim 46 \%\)$
Hence the answer is (B).
gmatclubot
Pat takes 4 hours to complete a work, Quinn takes 6 hours and Rob ta [#permalink]
02 Feb 2025, 07:41
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