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Two machines working on a task can complete a job in 2 hours and 5 hou
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22 Nov 2021, 08:38
22 Nov 2021, 08:38
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Question Stats:
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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
(A) 2/5
(B) 7/10
(C) 10/7
(D) 3/2
(E) 5/2
Two machines working on a task can complete a job in 2 hours and 5 hou
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22 Nov 2021, 08:51
22 Nov 2021, 08:51
1
Time taken by Machine 1 to complete the task, \(t_1 = 2 hr\)
Time taken by Machine 2 to complete the task, \(t_2 = 5 hr\)
Time taken when both machines work together, \(T = \frac{t_1t_2}{t_1 + t_2} = \frac{2*5}{2 + 5} = \frac{10}{7}hrs\)
You can remember that as a general formula for such questions
Hence, Answer is C
Time taken by Machine 2 to complete the task, \(t_2 = 5 hr\)
Time taken when both machines work together, \(T = \frac{t_1t_2}{t_1 + t_2} = \frac{2*5}{2 + 5} = \frac{10}{7}hrs\)
You can remember that as a general formula for such questions
Hence, Answer is C
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Re: Two machines working on a task can complete a job in 2 hours and 5 hou
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22 Nov 2021, 09:33
22 Nov 2021, 09:33
Carcass wrote:
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
(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: C
