A tank has two pipes entering it.when operating together,they fill the tank in 40 minutes.operating independently,one of the pipes fills the tank 60 minutes faster than the other one does. calculate the time taken by each pipe to fill the tank on its own.

Tank #1 = T min.

Tank #2 = (T+60) min.

T*(T+60)/(T+T+60) = 40 min
(T^2+60T)/(2T+60) = 40
T^2+60T = 80T+2400
T^2 - 20T - 2400 = 0
Use Quadratic Formula.
T = 60 min.
T + 60 = 60 + 60 = 120 min.

Let's assume that one of the pipes (the faster one) takes x minutes to fill the tank on its own. This means that the other pipe (the slower one) takes x + 60 minutes to fill the tank on its own.

To find the combined rate of the two pipes, we can take the reciprocal of the time taken to fill the tank. So, the combined rate can be calculated as 1/40 (since they fill the tank in 40 minutes when operating together).

Now, let's calculate the rate of each pipe separately. The rate of the faster pipe will be 1/x (since it takes x minutes to fill the tank on its own). Similarly, the rate of the slower pipe will be 1/(x + 60).

Since the pipes are operating simultaneously, their rates add up to the combined rate. So, we can set up the following equation:

1/x + 1/(x + 60) = 1/40

To simplify this equation, let's find a common denominator. Multiplying all terms by 40x(x + 60), we get:

40(x + 60) + 40x = x(x + 60)

Expanding and simplifying:

40x + 2400 + 40x = x^2 + 60x

Combining like terms:

80x + 2400 = x^2 + 60x

Rearranging to form a quadratic equation:

x^2 + (60 - 80)x - 2400 = 0

We can now solve this quadratic equation to find the value of x. The solutions represent the time taken by each pipe to fill the tank on its own.