Two pumps work together to fill the pool with water in 12 hours. in how many hours can the first

Two pumps work together to fill the pool with water in 12 hours. in how many hours can the first pump fill the pool with water, working separately, if it is known that it fills half of the pool with water 5 hours faster than the second pump?

12 hours is the time it takes two pumps to fill the pool.

Let’s conditionally denote the time during which the first pump will fill the pool – a hours, then:

(a + 10) is the time it takes for the second pump to fill the entire pool (it fills half of it in 5 hours faster).

(1 / a) + 1 * (a + 10) = 1/12.

12 * (a + 10) + 12a = a * (a + 10).

12a + 120 + 12a = a ^ 2 + 10a.

a ^ 2 – 14a – 120 = 0.

a1 = 20.

a2 = – 6 (not suitable).

Solution: The first pump will fill in 10 hours and the second pump in 20 hours.