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Machines X and Y run at different constant rates, and machine X can co

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Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 21 Sep 2019, 05:26
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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

PS56502.01
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Re: Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 21 Sep 2019, 05:35
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3
rate of X = 1/9
completed work 1/9 * 3 ; 1/3 job
left with 2/3 work which is completed in 4 hrs more working together X&Y ;
2/3 = (1/9+1/y)*4
solve y=18
IMO A


gmatt1476 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

PS56502.01
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Re: Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 21 Sep 2019, 05:32
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gmatt1476 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

PS56502.01


Let Y alone takes 'a' hours to complete

Fraction of Work done by X in 3 hours = 3/9 = 1/3
Remaining 4 hours, work by X & Y together = 4/9 + 4/a

--> 1/3 + 4/9 + 4/a = 1
--> 7/9 + 4/a = 1
--> 4/a = 2/9
--> a = 18

IMO Option A

Pls Hit kudos if you like the solution
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Re: Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 07 Apr 2020, 09:46
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gmatt1476 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

PS56502.01


Another 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

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Brent
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Re: Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 07 Apr 2020, 09:54
Machine Y does (1-7/9) = 2/9 of the job in 4 hours.
Therefore machine Y will do total job in 9/2 ×4 = 18 hours

Option A is the answer.

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Re: Machines X and Y run at different constant rates, and machine X can co  [#permalink]

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New post 01 May 2020, 22:42
Hi, i did as follows:

3/9+4(1/9+1/y)=1
3 hours A alone and then 4 hours both together equals 1

im not getting an answer with this though. could some help point the error?
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Re: Machines X and Y run at different constant rates, and machine X can co   [#permalink] 01 May 2020, 22:42

Machines X and Y run at different constant rates, and machine X can co

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