An empty pool is filled through the first pipe 5 hours faster than through the second.

An empty pool is filled through the first pipe 5 hours faster than through the second. When both pipes work together, the pool is filled in 6 hours. how many hours it takes to fill the pool through each pipe separately.

Let the pool fill up through the first pipe in x hours, then through the second pipe in (x + 5) hours. Then in an hour 1 / x part of the pool is filled through the first pipe, and through the second 1 / (x + 5) part of the volume. Let’s make an equation for the joint work of both pipes.

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

Let’s bring the fractions to a common denominator and equate the numerators.

6 (x + 5) + 6x = x (x + 5).

x ^ 2 + 5x – 12x – 30 = 0;

x ^ 2 – 7x – 30 = 0;

D = 7 * 7 + 4 * 30 = 49 + 120 = 169 = 132.

x = (7 + 13) / 2 = 10 hours.

10 + 5 = 15 hours (second tube).

Answer: the pool can be filled through the first pipe in 10 hours, through the second pipe – in 15 hours.