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# Pump A, pumping water at a constant rate, can fill a certain swimm....

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Re: Pump A, pumping water at a constant rate, can fill a certain swimm.... [#permalink]

bwashburn15 wrote:
­Pump A, pumping water at a constant rate, can fill a certain swimming pool in 6 hours.  Pump B, pumping water at a constant rate, can fill the same pool in 4 hours.  If both pumps begin filling the pool simultaneously when the pool is empty and pump B breaks down 1 hour after they begin filling the pool, how many hours will it take pump A alone to finish filling the pool?

A. 1 2/5
B. 2 1/3
C. 3 1/2
D. 4
E. 4 4/5
­

Solution:   Let's take the rate of pump A = 1/6
Rate of pump B = 1/4
When both pumps were working together the time taken to fill the pool = was 1 hour
So, by using the matrix approach we can solve this very easily

The extra time it took for pump A to fill the pool = t + 1

Work of pump A to fill the tank                          = 1/6t +1/6 = t+1/6
Work of pump B to fill the tank                          = 1/4 * 1     = 1/4

If we combine the work of both pumps then we have

Work of Pump A + Work of Pump B  = 1

t/6+1/6 + 1/4 = 1 ---> 3 1/2

Option C

Re: Pump A, pumping water at a constant rate, can fill a certain swimm.... [#permalink]
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