Question

· A swimming pool is filled by 3 pipes. the first
two pipes together as same time as third pipe
to fill the pool. The second pipe alone can fill 5
hour faster than first pipe and 4 hours slower
third pipe. Find the time in which second and
third together can fill the pool ?​

Answer 1

Answer:

Let V be the volume of the pool and x the number of hours required by the second pipe alone to fill the pool. Then, the first pipe takes (x+5) hours, while the third pipe takes (x−4) hours to fill the pool. So, the parts of the pool filled by the first, second and third pipes in one hour are respectively

x+5

V

,

x

V

,

x−4

V

Let the time taken by the first and second pipes to fill the pool simultaneously be t hours.

Then, the third pipe also takes the same time to fill the pool

∴(

x+5

V

+

x

V

)t= Volume of the pool

Also,

x−4

V

t= Volume of the pool

⇒(

x+5

V

+

x

V

)t=

x−4

V

t⇒

x+5

1

+

x

1

=

x−4

1

⇒(2x+5)(x−4)=x

2

+5x⇒x

2

−8x−20=0⇒x

2

−10x+2x−20=0⇒(x−10)(x+2)=0

⇒x=10orx=−2

But x cannot be negative. So x=10

hence the timings required by first, second and third pipes to fill the pool individually are 15 hours, 10 hours and 6 hours respectively.

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