Two pipes, working simultaneously, fill the pool in 12 hours. The first pipe fills the pool 10 hours faster than the second.

Two pipes, working simultaneously, fill the pool in 12 hours. The first pipe fills the pool 10 hours faster than the second. How many hours does the second pipe take to fill the pool? solve using a system of equations.

1) If x is the time during which the first pipe fills the pool, then the second pipe will fill it in (x + 10) hours. The first pipe in 1 hour can fill 1 / x part of the pool, and 1 / (x + 10) is the part of the pool that the second pipe fills.

2) In 1 hour, both pipes together will fill [1 / x + 1 / (x + 10)] = (2 * x + 10) / x * (x + 10) part of the pipe.

3) In 12 hours, both pipes together will fill the entire pool, which we took as conditional 1. We obtain the equation:

12 * (2 * x + 10) / x * (x + 10) = 1; 12 * 2 * (x + 5) = x ^ 2 + 10 * x; x ^ 2 + 10 * x – 24 * x – 120 = 0; x ^ 2 – 14 * x – 120 = 0; x1 = 20; x2 = -6; take: x = 20, y = 30.