Working independently, Susan can perform a certain task in 6 hours and

Question

Working independently, Susan can perform a certain task in 6 hours and Tom can perform it in 7 hours. If Susan and Tom work together on the task for 3 hours, at which point Susan leaves, how many hours will it take Tom to complete the task alone?

A. 1/14
B. 13/14
C. 1/2
D. 29/42
E. 1

A. 1/14
B. 13/14
C. 1/2
D. 29/42
E. 1

gmatophobia · Answer

Let's assume that the task requires 42 units of work.

Number of units of work done by Susan per hour = 7 
 Number of units of work done by Tom per hour = 6

Together, Susan and Tom will complete 7 + 6 = 13 units of work

In hours, they complete 3 * 13 = 39 units of work.

Remaining units = 42-39 = 3

Time Tom would require to complete the task alone =  \frac{3}{6} = \frac{1}{2}

Option C

Archit3110 · Answer

Combined rate is 13/42
Rate is 1/7 & 1/6
Let unit work 1
So in 3 hours work done js 13/14
Work left to be done is 1/14
Time it will take Tom to complete 
1/14 ×7= time
1/2 option C

Posted from my mobile device

Kimberly77 · Answer

gmatophobia  great explanation. not sure why is time Tom required is 3/6 and not 7 ( Tom's hr)
Could you help clarify? Thanks

gmatophobia · Answer

Hello  Kimberly77

Thanks for reaching out.

In the explanation posted above, we have taken the LCM of Susan's and Tom's time to calculate the total work.

We have assumed that the total work equals 42 units. Therefore, Tom can complete  \frac{42}{7} = 6  units of work in one hour.

After Tom and Susan have worked for 3 hours, 39 units of the 42 units of work are completed. Hence, 3 units of work remain.

As Tom can complete 6 units of work in on hour, he completes 3 units of work in  \frac{3}{6}  hours.

Kimberly77 · Answer

Get it now thanks gmatophobia for your greaat explanation and quick reply

buzz111 · Answer

The question stem says Susan 6hrs and Tom 7hrs, but you are dividing 3/6. It asked for Tom's time requirement to complete the task.

SSM24 · Answer

youve mixed up tom and susan's hours

gmatophobia · Answer

SSM24  - Apologies, I couldn't follow your concern well. Can you provide more context?

Are you referring to this part of the solution -

gmatophobia · Answer

buzz111  You may want to refer to the explanation provided  here

Working independently, Susan can perform a certain task in 6 hours and

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