The first pipe flows 4 liters of water per minute less than the second pipe. How many liters of water per

The first pipe flows 4 liters of water per minute less than the second pipe. How many liters of water per minute does the second pipe pass if it fills the 480 liter tank 4 minutes faster than the first pipe?

Suppose that the second pipe passes x liters of water per minute, then the first pipe passes per minute (x – 4) liters of water.

It will take 480 / x minutes to fill the tank with a volume of 480 liters through the second pipe.

The same tank through the first pipe will fill 480 / (x – 4) minutes.

By the condition of the problem we get the equation:

480 / (x – 4) = (480 / x) + 4,

480 / (x – 4) = (480 + 4 * x) / x,

480 * x = (480 + 4 * x) * (x – 4),

480 * x = 480 * x – 480 * 4 + 4 * x ² – 16 * x,

4 * x ² – 16 * x – 1920 = 0,

x² – 4 * x – 480 = 0.

Let’s solve this quadratic equation:

D = (- 4) ² – 4 * 1 * (-480) = 16 + 1920 = 1936, then

x = (4 + 44) / 2 = 24 and x = (4 – 44) / 2 = – 20.

Since the rate of water inflow cannot be negative, the only solution is x = 24.

Answer: 24 liters per minute.