The pool with a volume of 1m3 is filled with two pumps at the same time. The first pump pumps over 1m3 more

The pool with a volume of 1m3 is filled with two pumps at the same time. The first pump pumps over 1m3 more in 1 hour than the second. Find the time it takes for each pump individually to fill the pool if the first pump needs 5 minutes less than the second.

Let us denote by the variable x the number of cubes that the second pump pumps in an hour.

Then the first pump pumps in an hour (x + 1).

Knowing that the first pump needs 5 minutes less to fill the pool, let’s make an equation and find in how many minutes each pump will fill the pool:

1 / x – 1 / (x + 1) = 5/60;

x + 1 – x = x (x + 1) / 12;

x ^ 2 + x – 12 = 0;

D = 1 – 4 (-12) = 49 = 7 ^ 2;

x1 = (-1 + 7) / 2 = 3;

x2 = (- 1 – 7) / 2 = -4.

60 * 1/3 = 20;

60 * 1 / (3 + 1) = 15.

Answer: The first pump needs 15 minutes, the second 20.