Two women, A and B working separately can mow a field in 8

Question

Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

A. 18:00 PM
B. 18:15 PM
C. 18:25 PM
D. 18:30 PM
E. 18:45 PM

Bunuel · Accepted Answer

In 1 hour A does \frac{1}{8}=\frac{3}{24} th of the whole job and B \frac{1}{12}=\frac{2}{24} th of the whole job (common denimnator makes the following calculations easier). So in 2 hours they do \frac{3}{24}+\frac{2}{24}=\frac{5}{24} th of the whole job (so at this stage we know that time needed to do the whole job will be less than 5 2-hour periods or 10 hours, as 5*\frac{5}{24}=\frac{25}{24}>1 ). Now in 8 hours (4 two hour periods) they do 4*\frac{5}{24}=\frac{20}{24} th of the whole job. Then will be A's turn and by the end of 9 hours \frac{20}{24}+\frac{3}{24}=\frac{23}{24} th of the job will be done and \frac{1}{24} th will be left, which can be done by B (as it's B's turn now) in 1/2hours (30 minutes). So total time 8+1+\frac{1}{2}=9\frac{1}{2} , hence they will finish at 9:00AM+9\frac{1}{2}=18:30PM . Similar problem: pipes-and-cisterns-93482.html#p719223 Hope it's clear.

Bunuel · Answer

2 hours is 1 cycle - a period of time when both A and B worked once. As long as we know what part of the job is done in one cycle we can find in which range to look for the correct answer. We had that the period of time must be less than 5 cycles (10 hours) and then we started calculating directly for 4 cycles, which saved us some time.

mikioso · Answer

dont use the algebric way on this one. just draw a table and add the values: a=3/24 an b=2/24.

RenukaD · Answer

Thanks Bunuel, One more question my understanding for "If they work together in stretches on 1 hr alternately," sentence was, they will work alternatively lets say A will work at 9:00 AM and B will start at 10:00AM. If my understanding is correct the how come 9th hr will come for A?

RenukaD · Answer

It will be helpful Mikioso, if u can explain that method.

skovinsky · Answer

Hi,

A goes first, so A does the 1st hour, 3rd hour, 5th hour, 7th hour, 9th hour, ...

RenukaD · Answer

Thanks skovinsky, now I got it

GMATaddict · Answer

mmm... the working alternately thing is kind of a pain.

So in the first hour A did 1/8th of the job, & in the 2nd hour B did 1/12th of the job. In 2 hours, they did 5/24 of the job together. Meaning in 8 hours they would have completed (5/24)X4=20/24.

In the 9th hour, A is on shift again & completes 1/8th (or in other words, 3/24th) of the job, so we're now that 23/24. In the 10th hour, B completes the remainder 1/24th. We know B can do 1/12th in 1 hour, so she'll only take half the hour to complete 1/24th of the job.

We do some counting with our fingers & see that it takes 9.5 hours. So starting at 0900 (9am in civilian time), we would complete the job at 18:30 or 6:30pm.

Kind of a pain in the ass but doable in 2 minutes.

prasannajeet · Answer

Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

HI Bunnel 
Please clarify me where I have gone wrong

Rate A-1/8
Rate B-1/12

let say A works for 4 hour and rate is 1/8 so total job done = 1/8*4=1/2
Similarly let say B works for 6 hour and rate is 1/12 so total job done=1/12*6=1/2

So both can finish the work in 10 hours if they work alternatively. 9.00 am+10 hour=19.00pm answer

Where i have gone wrong..............

Rgds
Prasannajeet

Bunuel · Answer

I think you misinterpreted the question. A and B work in shifts: A goes first and works for 1 hour, then goes B and works for 1 hour, ... Thus, for this scenario it's not possible A to work 4 hours and B 6 hours.

GMATDemiGod · Answer

hey Bunuel,

thanks for the solution,

I just have one questions

if the rate came to 5/25 instead of 5/24, would the answer me 10 hours?

I stopped my solution at time = 24/5 = about 9.8 hours. Not sure what alerts us to solve further for the breakdown.

mvictor · Answer

add the answers to the question
the answer should be 18:30
let's assume that the total work is 48
the A will do in 1 hour 6 parts of the work, B will do 4 parts of the work
2 hours - 10 parts of the work
4 hours - 20 parts
6 hours - 30 parts
8 hours - 40 parts
9 hours - 46 parts
9.5 hours - 48 parts

started at 9AM + 9.5hr = 18:30

GMATinsight · Answer

Answer: 9.5 hours Check the explanation as attached here Screenshot 2020-08-11 at 8.20.14 PM.png

Vector800 · Answer

Bunuel 
 chetan2u

I have done it in a slightly different approach and arrived at 9.6hrs.
What is wrong with my method?

In one hour:
A=1/8
B=1/12

So in 2 hours they finish
(1/8)+(1/12)=(5/24) of the work.

Total work to be done is 1.
Which is (24/24)
(5/24) of work is done in 1 two hour period
(24/24) of work will be done in how many two hour periods?

-> (24/24)/(5/24) = (24/5) = 4.8 two hour periods.
-> 4.8 two hour periods is equal to 9.6hrs.

But the answer y'all got is 9.5.

Where did i go wrong?

ankitgoswami · Answer

You cannot actually do it like this. Understand it this way - when you say 5/24 of the work was done in 2 hours, it means collectively they did that amount of work with their varying speeds. However, it does not mean that their speed was uniform throughout that 2-hour duration. A did the work faster than B during those 2 hours. Dividing by 5/24 does not take that into account. So you cannot directly divide it by 5/24.

However, what you can do is - you can get as close as possible to 1 by finding repetitions of 5/24, which are 4 (amounting to 8 hours). Add one hour of A = 20/24 + 1/8 = 23/24. Now the remaining is 1/24 which is half an hour's work of B. So total time = 8 + 1 + 0.5 = 9.5 hours

Kinshook · Answer

Given: Two women, A and B working separately can mow a field in 8 and 12 hrs respectively.

Asked: If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

Work done by A & B in 1 hour is 1/8 and 1/12 respectively

1/8 + 1/12 = 5/24

(1/8 + 1/12) + (1/8 + 1/12) + (1/8 + 1/12) + (1/8 + 1/12) = 20/24 = 5/6
Total time spent = 2*4 = 8 hours
Work done = 5/6

Remaining work = 1 - 5/6 = 1/6
Work done in 1 hour = 1/8
Remaining work = 1/6 - 1/8 = 1/24

Time taken to finish the remaining work = 12/24 = 1/2 hours

Total time taken to finish the complete work = 8 + 1 + 1/2 = 9 1/2 hours

Time when mowing will be finished = 9:00 + 9:30 = 18:30 hours = 6:30 PM

chetan2u · Answer

Had their working speed been equal, your answer would be correct, but that is not the case. 
The work done is more in the first one hour as compared to second hour. You cannot take it same for alternate hour.

Say he was left with 1/8 work after some 2-hr periods, then in next one hour he would have finished his work but if you take average it will be more than one hour.

HarshavardhanR · Answer

For this question, we can also take a clue from the choices. All choices are between 18:00 PM and 19:00 PM.

So, we already know that from  9:00 AM to 18:00 PM , A and B are working in alternate hours.

This is essentially 9 hours of work, with A, who started first, working 5 hours, and B working 4 hours.

Work done by A till 18:00 PM -> 5 x 1/8 = 5/8 of total work
Work done by B till 18:00 PM -> 4 x 1/12 = 1/3 of total work
Total Work done by 18:00 PM -> (5/8) + (1/3) = 23/24 of total work

Therefore, remaining work as of 18:00 PM -> 1 - 23/24 = 1/24 of total work.

Now, B starts working again at 18:00 PM.

In 1 hour, B can complete 1/12 i.e., 2/24 of the work. 
Then, to do the remaining work (1/24 of the work), B would need only 1/2 an hour.

So, the answer is  choice D (18:30 PM).

Hope this helps!
Harsha
GMAT Tutor | gmatanchor.com

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Two women, A and B working separately can mow a field in 8

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