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Working alone at their respective constant rates, Audrey can complete
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Updated on: 04 Jan 2024, 16:25
Updated on: 04 Jan 2024, 16:25
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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.
(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.
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.
Last edited by Carcass on 04 Jan 2024, 16:25, edited 1 time in total.
Fixed
Re: Working alone at their respective constant rates, Audrey can complete
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23 Jun 2019, 05:26
23 Jun 2019, 05:26
4
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.
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.
Re: Working alone at their respective constant rates, Audrey can complete
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23 Jun 2019, 05:57
23 Jun 2019, 05:57
Thanks Amorphous. Can you please tell why my approach is incorrect?
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