Question

Two pipes can fill a tank in 52

minutes if both are turned on. If only one is used, it would take 39

minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)

Answer 1

The larger pipe takes 13 minutes to fill the tank, so the smaller pipe takes 52 minutes.

Step-by-step explanation:

Let's assume the larger pipe can fill the tank in x minutes.

Therefore, the smaller pipe would take x+39 minutes to fill the tank.

Now, we know that the larger pipe can fill the tank in 52 minutes, so we can set up the equation:

x/52 + (x+39)/x = 1

Multiplying through by 52x gives:

x^2 + 39x - 52x = 0

Simplifying the equation, we get:

x^2 - 13x = 0

Factoring out x, we have:

x(x-13) = 0

So, x = 0 or x = 13.

Since time cannot be negative, the larger pipe can fill the tank in 13 minutes, and therefore, the smaller pipe would take 13+39 = 52 minutes.