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Frances can complete a job in 12 hours, and Joan can complete the same

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Bunuel
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Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   20 Dec 2019, 02:26
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Frances can complete a job in 12 hours, and Joan can complete the same job in 8 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?

A. 6 p.m.
B. 7 p.m.
C. 8 p.m.
D. 10 p.m.
E. 12 p.m.
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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   20 Dec 2019, 02:39
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Bunuel wrote:
Frances can complete a job in 12 hours, and Joan can complete the same job in 8 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?

A. 6 p.m.
B. 7 p.m.
C. 8 p.m.
D. 10 p.m.
E. 12 p.m.


Explanation:
F= 1/12
J=1/8

From 9am to 3pm = 6 hours.
F wil complete 1/2 work.
Remaining Half will be completed by J in 4 hours. He starts at 4pm will complete by 8pm.

IMO-C
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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   20 Dec 2019, 08:50
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\(F=1/12 \) and \(J=1/8\)

If F worked 6 hours, then he must have completed \(6*(1/12)=1/2\) of the work.

So in order to complete the other half of the job, J must work \((1/8)*t=1/2\) therefore \(t=4\).

So she will finish working at 8p.m. (Answer C)
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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   20 Dec 2019, 23:21
Rate of F =1/12

Rate of R = 1/8

Frances work for 6 hours (from 9 a.m. to 3 p.m.)

Work done by Frances in 6 hours = 1/12 of 6 = 1/2, Remaining work = 1/2

Remaining work done by Joan in 1/2 x 8/1 = 4 hours , that is, the work will be finished at 8 p.m.
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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   03 Aug 2020, 06:20
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Another method to do this would be using the fact that when 2 or more people work towards the completion of work, then the sum fractions of work done by each person is equal to 1. (1 means work is completed)

Let Joan take x hours to complete the work.

Work done by Frances in 1 hour = \(\frac{1}{12}\)

Fraction of work done by Frances in 6 hours (9am to 3pm) = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Work done by Joan in 1 hour = \(\frac{1}{8}\)

Fraction of work done by Joan in x hours = \(\frac{x}{8}\)

Therefore \(\frac{1}{2}\) + \(\frac{x}{8}\) = 1

\(\frac{4 + x}{8} \)= 1

4 + x = 8

x = 4 hours

Therefore Joan will finish the work at 8 pm

Option C

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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink] New post   21 May 2023, 09:27
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Re: Frances can complete a job in 12 hours, and Joan can complete the same [#permalink]
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