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# Two water pumps, working simlutaneosly at their respective

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Director
Joined: 06 Feb 2006
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Two water pumps, working simlutaneosly at their respective [#permalink]

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12 Nov 2006, 05:19
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Two water pumps, working simlutaneosly at their respective rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?

A)5
B)16/3
C)11/2
D)6
E)20/3

Finding x is easy, but i found difficulty in finding the total work done....

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Current Student
Joined: 29 Jan 2005
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12 Nov 2006, 06:40
Let Y be the rate of the faster pump in terms of the the slower pump:

3/2Y(Y)/3/2Y+Y=4 ---> 3/2Y^2=10Y ---> 3/2Y=10 ---> Y=20/3

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Director
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12 Nov 2006, 10:26
GMATT73 wrote:
Let Y be the rate of the faster pump in terms of the the slower pump:

3/2Y(Y)/3/2Y+Y=4 ---> 3/2Y^2=10Y ---> 3/2Y=10 ---> Y=20/3

A very unclear equation...

(3/2y)*y / (3/2y)+y=4?

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Manager
Joined: 13 Sep 2006
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12 Nov 2006, 17:02
I set up two equations and used the substitution method for this problem:

equation 1

1/x + 1/y = 1/4

equation 2

x = 1.5y

Solve for Y and you get 20/3..

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Manager
Joined: 10 Jul 2006
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12 Nov 2006, 18:24
Let x be the faster one, y is the slower machine.

Since the rate of the faster one is 3/2 of the slower machine and the rate is expressed as 1/x and 1/y for the 2 machine.
I have: 1/x = (3/2) (1/y) <=> y = (3x)/2 <1>
another equation is 1/x +1/y = 1/4 <2>

Substitute the value of y into the second equation and solve for x, that would be the number of hrs x will take to work alone (20/3)

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GMAT Club Legend
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12 Nov 2006, 20:21
Pump A - A hours to fill 1 pool --> 1/A pool in 1 hour
Pump B - B hours to fill 1 pool --> 1/B pool in 1 hour

Together, they can fill (A+B)/AB pool in 1 hour. They can fill AB/A+B hours, which is 4 hours.

AB/A+B = 4

Assuming B is faster, then A = 1.5B
1.5B^2/2.5B = 4
1.5B = 10
B = 20/3 hours

Kudos [?]: 438 [0], given: 0

12 Nov 2006, 20:21
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# Two water pumps, working simlutaneosly at their respective

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