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Two machines working on a task can complete a job in 2 hours and 5 hou 01 Nov 2021, 06:15
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C
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Two machines working on a task can complete a job in 2 hours and 5 hours, respectively. How many hours does it take the two machines, working together but independently, to complete the same task?

(A) 2/5
(B) 7/10
(C) 10/7
(D) 3/2
(E) 5/2
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C
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Two machines working on a task can complete a job in 2 hours and 5 hou Updated on: 11 Nov 2021, 12:47
Originally posted by BrentGMATPrepNow on 01 Nov 2021, 09:46.
Last edited by BrentGMATPrepNow on 11 Nov 2021, 12:47, edited 1 time in total.
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Bunuel
Two machines working on a task can complete a job in 2 hours and 5 hours, respectively. How many hours does it take the two machines, working together but independently, to complete the same task?

(A) 2/5
(B) 7/10
(C) 10/7
(D) 3/2
(E) 5/2
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Let's assign a "nice value" to the job.
We want a value that works well with 2 hours and 5 hours.
So let's say the job = making 10 widgets.

rate = output/time
One machine can complete the job in 2 hours.
10/2 = 5, so that machine makes widgets at a rate of 5 widgets per hour.

The other machine can complete the job in 5 hours.
10/5 = 2, so that machine makes widgets at a rate of 2 widgets per hour.

They're COMBINED rate = 5 widgets per hour + 2 widgets per hour = 7 widgets per hour.

Time = output/rate
Time for the COMBINED machines to make 10 widgets = 10/7 hours

Answer: C
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Two machines working on a task can complete a job in 2 hours and 5 hou 03 Nov 2021, 07:12
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BrentGMATPrepNow
Bunuel
Two machines working on a task can complete a job in 2 hours and 5 hours, respectively. How many hours does it take the two machines, working together but independently, to complete the same task?

(A) 2/5
(B) 7/10
(C) 10/7
(D) 3/2
(E) 5/2

Let's assign a "nice value" to the job.
We want a value that works well with 2 hours and 5 hours.
So let's say the job = making 10 widgets.

rate = output/time
One machine can complete the job in 2 hours.
10/2 = 5, so that machine makes widgets at a rate of 5 widgets per hour.

The other machine can complete the job in 5 hours.
10/5 = 2, so that machine makes widgets at a rate of 2 widgets per hour.

They're COMBINED rate = 5 widgets per hour + 2 widgets per hour = 7 widgets per hour.

Time = output/rate
Time for the COMBINED machines to make 10 widgets = 10/7 hours

Answer: B
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So its C right?

B says the inverse for time
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Two machines working on a task can complete a job in 2 hours and 5 hou 11 Nov 2021, 12:47
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SiddharthR


So its C right?
B says the inverse for time
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Yes, the answer is C.
My bad.
It's fixed now.

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Two machines working on a task can complete a job in 2 hours and 5 hou 11 Nov 2021, 17:14
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Given: Two machines working on a task can complete a job in 2 hours and 5 hours, respectively.

Asked: How many hours does it take the two machines, working together but independently, to complete the same task?

Work done by first machine in 1 hour = 1/2
Work done by second machine in 1 hour = 1/5
Work done by both machines in 1 hour = 1/2 + 1/5 = 7/10

Hours taken by both machines to complete the task = 10/7

IMO C
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Two machines working on a task can complete a job in 2 hours and 5 hou 11 Nov 2021, 23:41
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Let the machines be A and B respectively.

A can complete a task in 2 hours. B can complete the task in 5 hours.

So, A can complete \(\frac{1}{2}\) of the task in one hour. ---(i)
B can complete \(\frac{1}{5}\) of the task in one hour. ---(ii)

Here, working together but independently is what I feel as the confusing part.
Working together but independently is the same as working together.

So, working together, A and B can complete \(\frac{1}{5} + \frac{1}{2} = \frac{7}{10}\) of the task in one hour.

Similar to steps (i) and (ii), if they can complete \(\frac{7}{10}\) of the task in one hour, they can complete the whole task in \(\frac{10}{7}\) hours.

Answer is option C.


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