The pool is filled with water using two pipes. When the first pipe worked for 6 hours, it was closed

The pool is filled with water using two pipes. When the first pipe worked for 6 hours, it was closed, and the second pipe was opened. After 3 hours of operation of the second pipe, the pool was filled. In how many hours can each pipe fill, working separately, if the first needs 4 hours less than the second?

Let the pool be filled through the first pipe in x hours, then through the second in x + 4.

In one hour, 1 / x part of the total volume is filled through the first pipe, and the second pipe is 1 / (x + 4) part per hour.

Let’s draw up an equation for the sequential filling of the pool one by one through 1 and 2 pipes.

6 / x + 3 / (x + 4) = 1.

6 * (x + 4) + 3x = x * (x + 4).

6x + 24 + 3x = x ^ 2 + 4x.

x ^ 2 + 4x – 9x – 24 = 0.

x ^ 2 – 5x – 24 = 0.

Let’s solve the quadratic equation.

D = 5 * 5 + 4 * 24 = 25 + 96 = 121 = 112.

x = (5 + 11) / 2 = 16/2 = 8 hours through the first.

8 + 4 = 12 hours after the second.

Answer: 8 o’clock – first, 12 o’clock – second pipe.