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# Working at constant rate, pump X pumped out half of the water in a flo

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Intern
Joined: 23 Dec 2015
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Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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01 Aug 2016, 20:06
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Working at constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?

a. 10
b. 12
c. 14
d. 18
e. 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Aug 2016, 23:17, edited 1 time in total.
RENAMED THE TOPIC.
Intern
Joined: 04 May 2015
Posts: 2
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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01 Aug 2016, 22:35
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Here pump x was able to work 1/2 the job in 4 hrs.

so it would have taken the pump x to complete the task in 8 hrs. so 1/x=1/8.....eqn(1)

again x and y working independently doing the same work (1/2 of the work) take 3hrs.
so total task would take 6 hrs. 1/x+1/y=1/6.........eqn(2)

solve eqn 1 and eqn 2 to get y=24
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Joined: 02 Sep 2009
Posts: 43891
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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01 Aug 2016, 23:18
pravinpillai2015 wrote:
Working at constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?

a. 10
b. 12
c. 14
d. 18
e. 24

Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Math Expert
Joined: 02 Sep 2009
Posts: 43891
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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01 Aug 2016, 23:19
Bunuel wrote:
pravinpillai2015 wrote:
Working at constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?

a. 10
b. 12
c. 14
d. 18
e. 24

Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

Almost the same question to practice: working-alone-at-its-constant-rate-pump-x-pumped-out-of-the-water-216023.html

Hope it helps.
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Joined: 07 Dec 2014
Posts: 907
Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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02 Aug 2016, 11:33
rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
24 hours
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2082
Location: India
GPA: 3.12
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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21 Jan 2018, 12:01
pravinpillai2015 wrote:
Working at constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?

a. 10
b. 12
c. 14
d. 18
e. 24

If the pump X pumped out half the water in 4 hours, it will pump out the entire water in 8 hours.
Similarly, the pump Y was started and the two pumps operating together are able to pump out
the entire water in 3 hours.

Assume the total capacity of the pump to be 96 units.

So, the pump X must be pumping out 12 units/hour. Since, both the pumps working together
pump out the remainder of the water in 3 hours, their combined capacity will be 16 units/hour.
Hence, pump Y must be pumping out 4 units/hour.

Therefore, Pump Y alone will take $$\frac{96}{4}$$ = 24 hours(Option E)
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Intern
Joined: 30 Nov 2017
Posts: 21
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]

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15 Feb 2018, 08:56
Suppose X extracts x liters/hour, while Y extracts y liters/hour
In 4 hours, X extracts 4 x liters
This is half of the basement capacity. So, total volume of water in the basement = 8x liters

After 4 hours, Y was started as well. They flush the remaining 4 x in 3 hours.

In 3 hours, X and Y combined would flush 3*(x + y)

It is given that 3*(x + y) = 4x
This gives x = 3y

Operating alone how much would Y take?

Total water = 8x
Y's capacity = y liters/hour

So, time taken by Y = 8x/y

We know x = 3y
So, x/y = 3

So, time taken by Y = 8x/y = 8*3 = 24
Re: Working at constant rate, pump X pumped out half of the water in a flo   [#permalink] 15 Feb 2018, 08:56
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# Working at constant rate, pump X pumped out half of the water in a flo

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