Question

If a tank can be filled by three pipes in 4, 6, and 12 hours respectively, how long will it take to fill the tank when all three pipes are opened together?

Answer 1

When all three pipes are opened together, it will take 2 hours to fill the tank.

Step-by-step explanation:

To find out how long it will take to fill the tank when all three pipes are opened together, we need to calculate their combined rate of filling the tank per hour. Let's denote the rate of the first pipe as R1, the rate of the second pipe as R2, and the rate of the third pipe as R3.

Given that pipe 1 can fill the tank in 4 hours, pipe 2 can fill the tank in 6 hours, and pipe 3 can fill the tank in 12 hours, we can calculate their rates as:

R1 = 1/4 tank per hour

R2 = 1/6 tank per hour

R3 = 1/12 tank per hour

Now, to find the combined rate when all three pipes are opened together, we simply add up their individual rates:

R_combined = R1 + R2 + R3 = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12 = 1/2 tank per hour

Therefore, it will take 2 hours to fill the tank when all three pipes are opened together.