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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Detailed Solution

Given that 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.
Assume that the pipe having the large diameter takes x hours to completely fill up the swimming pool.
Therefore, the pipe having the smaller diameter will take

(x + 10)

hours to fill the pool.
Thus, the part of the pool filled by the pipe with the larger diameter in 1 hour =

\frac{1}{x}

Again,
The part of the pool filled by the pipe with the smaller diameter in 1 hour =

\frac{1}{x + 10}

According to the given condition,
Question Image

⇒ x + 4 = 0 or x − 20 = 0 ⇒ x = − 4, 20

But the time taken cannot be negative.
So, the number of hours taken by the pipe with the larger diameter to fill up the pool completely is,
20 hours
Again, the time taken by the pipe with the smaller diameter to fill up the pool completely,