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Machines X and Y run at different constant rates, and machin
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24 Apr 2020, 05:52
24 Apr 2020, 05:52
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82% (02:37) correct
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Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
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Posts: 6218
Given Kudos: 136
Re: Machines X and Y run at different constant rates, and machin
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24 Apr 2020, 07:33
24 Apr 2020, 07:33
1
Carcass wrote:
Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
One way to solve this question is to assign a nice value to the job.
So, we want to use a value that works well with the given numbers in the question (9, 3 and 4 hours).
Since 36 is the least common multiple of 9, 3 and 4, let's say the entire job consists of making 36 widgets
Machine X can complete a certain job in 9 hours
So, Machine X's RATE = 36/9 = 4 widgets per hour
Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours.
At its rate of 4 widgets per hour, Machine X would have produced 12 widgets in 3 hours
36 - 12 = 24
So, after the first 3 hours, the two machines would need to produce the 24 remaining widgets in the job
Since the two machines COMBINED produced the remaining 24 in 4 hours, their COMBINED RATE = 24/4 = 6 widgets per hour
We can write: (Machine X's rate) + (Machine Y's rate) = 6 widgets per hour
Substitute to get: 4 + (Machine Y's rate) = 6 widgets per hour
From this, we can see that Machine Y's rate = 2 widgets per hour
How many hours would it have taken machine Y, working alone, to complete the entire job?
time = output/rate
So, time = 36/2 = 18
Answer: A
Cheers,
Brent
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Status:Founder & Quant Trainer
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Re: Machines X and Y run at different constant rates, and machin
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03 Feb 2021, 04:35
03 Feb 2021, 04:35
We know, Rate = Work/Time
Also, that both the machines completed the Work
So, W1 + W2 = 1
or R1T1 + R2T2 = 1
Machine 1 worked for a total of 7 hours with the Rate of (1/9), whereas, Machine 2 worked for 4 hours with the Rate of X (assume)
7/9 + 4/X = 1
Solve for X = 18
Hence, option A
Also, that both the machines completed the Work
So, W1 + W2 = 1
or R1T1 + R2T2 = 1
Machine 1 worked for a total of 7 hours with the Rate of (1/9), whereas, Machine 2 worked for 4 hours with the Rate of X (assume)
7/9 + 4/X = 1
Solve for X = 18
Hence, option A
