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Working alone at their respective constant rates, Audrey can complete

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saurabhhjjain
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Working alone at their respective constant rates, Audrey can complete [#permalink] New post   Updated on: 04 Jan 2024, 16:25
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10% (02:56) correct 90% (02:45) wrong based on 20 sessions

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Q : Working alone at their respective constant rates, Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audrey and Ferris worked together on the job and completed it in 2 hours, but while Audrey worked this entire time, Ferris worked for some of the time and took 3 breaks of equal length. How many minutes long was each of Ferris's break?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Can anybody help me in solving this problem.

My solution :

Lets suppose total work is W.
Audrey working rate : W/4
Ferris working rate : W/3
If both work together, then working rate : (W/4) + (W/3) = 7W/12

If both work together, work W can be done in 12/7 hours.
Extra time taken = total break time taken by Ferris = (2*60 - 12*60/7) minutes = 120/7 minutes.

One interval length is = (120/7)/3 = 40/7. Closest answer is (A) 5 which is incorrect.
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B

Originally posted by saurabhhjjain on 23 Jun 2019, 04:14.
Last edited by Carcass on 04 Jan 2024, 16:25, edited 1 time in total.
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amorphous
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   23 Jun 2019, 05:26
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Audrey can do 1 work in 4 hrs
or, Audrey can do \(\frac{1}{4}\) work in 1 hrs.
She works for 2 hrs so
Audrey can do \(\frac{2}{4}\) work in 2 hrs.
Hence Audrey can do \(\frac{1}{2}\) work in 2 hrs.

The total work was completed in 2 hrs, if Audrey completed \(\frac{1}{2}\) the work then the other \(\frac{1}{2}\) must be completed by Ferris.

We know,
Ferris can do 1 work in 3 hrs. If Ferris only did 1/2 the work then,
Ferris did \(\frac{1}{2}\) work in \(\frac{3}{2}\) hrs.
Therefore Ferris completed \(\frac{1}{2}\) the remaining work in 1.5 hrs.
This gives Ferris a spare time of 0.5 hrs or 30 mins. If Ferris took three breaks of equal length then he must have taken a break of 10 minutes each.
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   23 Jun 2019, 05:57
Thanks Amorphous. Can you please tell why my approach is incorrect?

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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   23 Jun 2019, 07:15
"Extra time taken = total break time taken by Ferris = (2*60 - 12*60/7) minutes = 120/7 minutes."

I don't understand what you have done here.

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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   28 Jun 2019, 07:19
amorphous wrote:
"Extra time taken = total break time taken by Ferris = (2*60 - 12*60/7) minutes = 120/7 minutes."

I don't understand what you have done here.

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Since they could complete a work in 12/7 hour if worked together but they actually completed it in 2 hours. So extra time taken ((2*60 - 12*60/7) mins) should be equal to total break time for ferris.
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   28 Jun 2019, 08:09
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saurabhhjjain wrote:
Q : Working alone at their respective constant rates, Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audrey and Ferris worked together on the job and completed it in 2 hours, but while Audrey worked this entire time, Ferris worked for some of the time and took 3 breaks of equal length. How many minutes long was each of Ferris's break?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours.
So, Audrey's RATE = 1/4 of the job per hour
And Ferris' RATE = 1/3 of the job per hour

Audrey and Ferris worked together on the job and completed it in 2 hours, but while Audrey worked this entire time, Ferris worked for some of the time and took 3 breaks of equal length.
Since Audrey works for the entire 2 hours, let's determine how much work she does.
At a rate of 1/4 of the job per hour, Audrey can complete 1/2 of the job in TWO hours.

This means Ferris must have completed the other 1/2 of the job

Time = output/rate
So, Ferris' work time = (1/2)/(1/3) = 3/2 hours = 90 MINUTES

So, at his normal rate of work, Ferris can complete his half of the job in 90 MINUTES, which meanshe rested for the other 30 minutes.


How many minutes long was each of Ferris's break?
Ferris took 3 breaks of equal length
If he rested for a TOTAL of 30 minutes, each break was 10 minutes long.

Answer: B

Cheers,
Brent
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   28 Jun 2019, 08:12
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saurabhhjjain wrote:
Thanks Amorphous. Can you please tell why my approach is incorrect?

Posted from my mobile device Image


Your approach doesn't work, because it assumes that BOTH people worked together to complete the job in 120/7 minutes, and then they BOTH rested for the remaining 20/7 minutes.
In actuality, Ferris is the only person who rested.

Cheers,
Brent
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   29 Jun 2019, 02:08
Thank you Brent.
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   15 Aug 2019, 05:09
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I've attached how I did it.
Attachments

daum_equation_1565874520871.png
daum_equation_1565874520871.png [ 297.68 KiB | Viewed 11597 times ]

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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   19 Aug 2019, 10:20
tricky question. thanks for the solution!
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Re: Working alone at their respective constant rates, Audrey can complete [#permalink] New post   15 Dec 2024, 04:51
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