# To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled.

in Maths
To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

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Solution:

Let the time taken by larger pipe alone to fill the tank= x hours

Therefore, the time taken by the smaller pipe = x+10 hours

Water filled by larger pipe running for 4 hours = 4/x litres

Water filled by smaller pipe running for 9 hours = 9/x+10 litres

We know that 4/x + 9/(x+10) = 1/2

Which on simplification gives:

x2−16x−80=0

x2−20x + 4x−80=0

x(x-20) + 4(x-20)= 0

(x +4)(x-20)= 0

x=- 4, 20

x cannot be negative.

Thus, x=20

x+10= 30

Larger pipe would alone fill the tank in 20 hours and smaller pipe would fill the tank alone in 30 hours.