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Machine A takes 10 hours to complete a certain job and starts that job
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24 Aug 2022, 06:40
24 Aug 2022, 06:40
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Question Stats:
60% (02:35) correct
40% (02:46) wrong based on 30 sessions
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Machine A takes 10 hours to complete a certain job and starts that job at 9AM. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours
(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: Machine A takes 10 hours to complete a certain job and starts that job
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24 Aug 2022, 07:12
24 Aug 2022, 07:12
1
Equation of work done
Work = Rate *Time
Let Rate of A be a
Given, A takes 10 hours to complete a certain job
Work = a * 10
1 = a * 10
a = 1/10
Work done by A from 9 AM to 10 AM
Work = (1/10)* 1 = 1/10
Work Left = 1-1/10 = 9/10
Let Rate of B be b
9/10 = ( a+b ) * (Time between 10 AM to 5 PM)
9/10 = ( 1/10 +b) * 7
b = 2/70
Time that B would take working alone :
1 = b * t
t = 1/b = 70/2 = 35 hours
Answer is E
Work = Rate *Time
Let Rate of A be a
Given, A takes 10 hours to complete a certain job
Work = a * 10
1 = a * 10
a = 1/10
Work done by A from 9 AM to 10 AM
Work = (1/10)* 1 = 1/10
Work Left = 1-1/10 = 9/10
Let Rate of B be b
9/10 = ( a+b ) * (Time between 10 AM to 5 PM)
9/10 = ( 1/10 +b) * 7
b = 2/70
Time that B would take working alone :
1 = b * t
t = 1/b = 70/2 = 35 hours
Answer is E
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Re: Machine A takes 10 hours to complete a certain job and starts that job
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24 Aug 2022, 08:56
24 Aug 2022, 08:56
Carcass wrote:
Machine A takes 10 hours to complete a certain job and starts that job at 9AM. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours
(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours
One approach:
Working ALONE Machine A takes 10 hours to do the job.
With Machine B's help, the job took 8 hours to complete.
So, Machine B saved Machine A 2 hours of work.
In other words, during the 7 hours that Machine B was helping, Machine B did the work that would have taken Machine A an extra 2 hours to complete.
So, it takes Machine B 7 hours to complete the same amount of work that it takes Machine A to complete in 2 hours.
So, it takes Machine B 7/2 times as long to complete what Machine A can complete
It takes Machine A 10 hours to do the job.
So, the time it takes Machine B to do the job = (10)(7/2) = 35 = E
Cheers,
Brent
