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Adam and Bryan can complete a job in 48 hours working together.

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Adam and Bryan can complete a job in 48 hours working together.  [#permalink]

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New post Updated on: 14 Apr 2019, 08:25
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Question Stats:

18% (03:45) correct 82% (02:37) wrong based on 11 sessions

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Adam and Bryan can complete a job in 48 hours working together. On an occasion, Adam worked alone for half the time Bryan takes to complete the work, and then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work. When Bryan stopped, five-sixths of the work was done. What is the least time that will be taken either by Adam or Bryan to complete the work alone?

A. 96 hours
B. 80 hours
C. 60 hours
D. 72 hours
E. 120 hours

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Originally posted by DisciplinedPrep on 11 Apr 2019, 23:11.
Last edited by DisciplinedPrep on 14 Apr 2019, 08:25, edited 1 time in total.
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Re: Adam and Bryan can complete a job in 48 hours working together.  [#permalink]

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New post 11 Apr 2019, 23:40
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DisciplinedPrep wrote:
Adam and Bryan can complete a job in 48 hours working together. On an occasion, Adam worked alone for half the time Bryan takes to complete the work, and then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work. When Bryan stopped, five-sixths of the work was done. What is the least time that will be taken either by Adam or Bryan to complete the work alone?

A. 96 hours
B. 80 hours
C. 60 hours
D. 72 hours
E. 120 hours



Go step wise and you will get the answer..
Let the time be A and B for Adam and Bryan to complete a job alone, so \(\frac{1}{A}+\frac{1}{B}=\frac{1}{48}\)..

Step 1 : Adam worked alone for half the time Bryan takes to complete the work
So, Adam works for B/2 hours and he will complete the work in \(\frac{1}{A}*\frac{B}{2}\)

Step 2 : then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work.
So, Bryan works for A/3 hours and he will complete the work in \(\frac{1}{B}*\frac{A}{3}\)

Step 3 : When Bryan stopped, five-sixths of the work was done.
so \(\frac{B}{2A}+\frac{A}{3B}=\frac{5}{6}.....3B^2+2A^2=5AB.....2B^2+2A^2-4AB-AB+B^2=0.......2(B-A)^2+B(B-A)=0....(B-A)+(2B-2A+B)=0....(B-A)+(3B-2A)=0\)


So, two cases..
(I) B=A, then \(\frac{1}{B}+\frac{1}{B}=\frac{1}{48}\)....B=96
(II) 3B=2A or A=3B/2, then \(\frac{2}{3B}+\frac{1}{B}=\frac{1}{48}........\frac{5}{3B}=\frac{1}{48}..... B=\frac{48*5}{3}=16*5=80\)

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Re: Adam and Bryan can complete a job in 48 hours working together.   [#permalink] 11 Apr 2019, 23:40
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Adam and Bryan can complete a job in 48 hours working together.

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