Frances Can Complete a Job in 12 hours, and Joan Can Complete the Same Job in 8 Hours GMAT Problem Solving

Question: 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?

6 p.m.
7 p.m.
8 p.m.
10 p.m.
12 p.m.

Correct Answer: C

Solution and Explanation
Approach Solution 1:
Considering the given case scenario of two workers Frances and Joan, it can be identified that Frances can work for 12 hours to complete a job. Joan can complete the same job in 8 hours. This can be implied as-

Frances- 1/12
Joan- 1/8

Based on the given scenario, Frances worked from 9am to and stopped working at 3pm. This equates to Frances working for 6 hours for the job. Accordingly, the amount of work he completed is equal to

1 ÷ 12 * 6 = ½

Joan is supposed to complete the work of Frances who did half of the work. This means that half of the remaining work is to be completed by Joan. accordingly, the time t that is required for Joan to complete the work can be equated with half of the work done by Frances. This equals to-

1 ÷ 8 * t= ½
\(\Rightarrow t=8* ^1/_2\)
\(\Rightarrow t=4\)

Hence, the time that would be required by Joan to complete the remaining half of the work is 4 hours. Accordingly, considering that Joan will start working from 4pm, his work would be completed by 8pm. Hence, C is the correct answer.

Approach Solution 2:
There is another method to solve the problem and get the answer.

One would be using the fact that when 2 or more people work towards the completion of work, then the sum of fractions of work done by each person is equal to 1. Here, 1 means work is completed by the person.
Let’s say, Joan takes x hours to complete the work which is what one needs to find from the problem.
The work completed by Frances in 1 hour is equal to = 1/12
Calculating the fraction of work done by Frances in 6 hours between 9am to 3pm is equal to 6/12. This implies that ½ of the work is completed by Frances in 6 hours.
Let us take the Work done by Joan in 1 hour is equal to ⅛, considering Joan takes 8 hours to complete his work.
Calculating the Fraction of work done by Joan in x hours will hence equal to x/8
Therefore, from the above evaluations it can be identified that when both the fractions are added, it gives the result one. This can be equated as-

1/2+ x/8= 1
4+x/8= 1
4 + x = 8

Accordingly, when the equation is resolved it gives the following results which can be identified as-
x = 4 hours
Therefore, Joan will take around four hours to complete the rest half of the work. While Joan will start his work from 4pm and take four hours to complete the work, it implies that the work will be completed by 8pm.
Hence, option C with 8pm as the answer is correct.

Approach Solution 3:
Frances worked 6 hours. Since she takes 12 hours for the whole job, she has done half the job.

Half the job remains for Joan to do.

Since Joan takes 8 hours for a whole job, she takes 4 hours for half a job.

So Joan will take 4 hours to finish the job.

Since she starts at 4 p.m., the job will be finished at 8 p.m.

“Frances can complete a job in 12 hours, and Joan can complete the same job in 8 hours”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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Frances Can Complete a Job in 12 hours, and Joan Can Complete the Same Job in 8 Hours GMAT Problem Solving

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