The pool is filled with two pipes operating simultaneously in 6 hours. How many hours can it take to fill the pool

The pool is filled with two pipes operating simultaneously in 6 hours. How many hours can it take to fill the pool, each pipe separately, if it is known that the first pipe fills the pool 5 hours earlier than the second pipe?

Let’s designate the time for which the first pipe fills the pool x hours, and the second x + 5 hours.

Working together, the first pipe will fill 6 / x part and the second 6 / (x + 5).

Let’s make an equation.

6 / x + 6 / (x + 5) = 1,

(6x + 30 + 6x) / x ^ 2 + 5x = 1,

6x + 30 + 6x = x ^ 2 + 5x,

-x ^ 2 + 7x + 30 = 0.

Let’s find the value “x” through the discriminant.

x = (-7 – √72 – 4 * (-1) * 30) / (2 * (-1)),

x = (-7 – √49 +120) / (- 2),

x = (-20) / (- 2) = 10 hours, during this time the first pipe will fill the pool.

The second pipe will fill the pool in 10 + 5 = 15 hours.