One water pipe fills a swimming bath in #x# hours. A second pipe takes #3# hours longer to fill the bath. The two pipes together fill the bath in two hours. How long will it take each pipe to fill the swimming bath separately?

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Answer 1 · 2018-08-13T14:30:00

I got #3 and 6# hours but check my maths anyway....

Have a look:

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Answer 2 · 2018-08-13T14:40:54

First pipe takes #3# hours to fill the pool and second pipe takes #6# hours to fill the pool.

First water pipe takes #x# hours to fill swimming bath

hence, in one hour, it fills #1/x# of the pool.

Second water pipe takes #x+3# hours to fill swimming bath

hence, in one hour, it fills #1/(x+3)# of the pool

In one hour they together fill #1/x+1/(x+3)=(2x+3)/(x^2+3x)#

as it should fill half of the pool, we have

#(2x+3)/(x^2+3x)=1/2#

or #x^2+3x=4x+6# i.e. #x^2-x-6=0#

i.e. #(x-3)(x+2)=0# and #x=3# or #-2#

As negative values are not permissible #x=3#

Hence first pipe takes #3# hours to fill the pool and second pipe takes #6# hours to fill the pool.