Two pipes fill the pool at the same time in 8 hours. If first the first pipe fills half of the pool

Two pipes fill the pool at the same time in 8 hours. If first the first pipe fills half of the pool, and then the second remaining half, then this takes 18 hours. How much will each pipe fill the pool?

Let the first pipe fill the entire pool in x hours, and the second pipe in y hours.
Let’s compose and solve a system of equations.

x / 2 + y / 2 = 18;

(1 / x + 1 / y) = 1/8.

Let’s simplify the expressions.

x + y = 36;

8y + 8x = xy.

x = 36 – y.

8y + 8 (36 – y) = y (36 – y).

8y + 288 – 8y = 36y – y ^ 2.

y ^ 2 – 36y + 288 = 0

D = 36 * 36 – 4 * 288 = 1296 – 1152 = 144 = 122.

y = (36 + 12) / 2 = 24;

x = 36 – 24 = 12.

Answer: one pipe will fill the pool in 24 hours, the other in 12 hours.