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.
1/x + 1/(x+10) = 1/12
x = 20
So, the pipes take 20 and 30 minutes, respectively.
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.