In a water refilling stationthe time that a pipe takes to fill a tank is 10 minutes more than the time that another pipe takes to fill the same tank. If the two . If the two pipes are open at the same time, they can fill the tank in 12 minutes. How many minutes does each pipe take to fill the tank?

If the faster pipe takes x minutes, then we have

1/x + 1/(x+10) = 1/12
x = 20

So, the pipes take 20 and 30 minutes, respectively.

Let's denote the time it takes for one pipe to fill the tank as x minutes. According to the given information, the other pipe takes 10 minutes more than x, so it takes (x + 10) minutes to fill the tank.

When both pipes are open, they can fill the tank in 12 minutes.

To solve this problem, we'll use the concept of rates. The rate at which the first pipe fills the tank is 1/x (1 tank in x minutes), and the rate at which the second pipe fills the tank is 1/(x + 10) (1 tank in (x + 10) minutes).

When both pipes are open, their rates of filling the tank are added up. So, the combined rate is 1/x + 1/(x + 10).

Since we know that they can fill the tank in 12 minutes, their combined rate is 1/12 (1 tank in 12 minutes).

Now we can set up the equation:
1/x + 1/(x + 10) = 1/12

To solve this equation, we'll multiply through by the common denominator, which is 12x(x + 10):
12(x + 10) + 12x = x(x + 10)

Simplifying this equation:
12x + 120 + 12x = x^2 + 10x
24x + 120 = x^2 + 10x
0 = x^2 - 14x - 120

Now we can solve this quadratic equation. By factoring or using the quadratic formula, we find that x = 20 or x = -6. Since time can't be negative, we disregard x = -6.

Therefore, one pipe takes 20 minutes to fill the tank, and the other pipe takes 20 + 10 = 30 minutes to fill the tank.