Two pipes open at the same time fill the pool in 5 hours. If the water flow through the first pipe is doubled

Two pipes open at the same time fill the pool in 5 hours. If the water flow through the first pipe is doubled, the pool will be filled in 4 hours. How long does it take for the first pipe to fill the pool.

Let us denote through x that part of the pool that the 1st pipe fills in 1 hour, and through y – that part of the pool that the 2nd pipe fills in 1 hour.

By the condition of the problem, two pipes open simultaneously fill the pool in 5 hours, therefore, the following relationship holds:

x + y = 1/5.

It is also known that if the water flow through the first pipe is doubled, then the pool will be filled in 4 hours, therefore, the following relationship takes place:

2x + y = 1/4.

We solve the resulting system of equations. Subtracting the first equation from the second, we get:

2x + y – x – y = 1/4 – 1/5;

x = 1/20.

Therefore, the first pipe fills the pool in 20 hours.

Answer: The first pipe fills the pool in 20 hours.