A swimming pool holds 600,000 liters of water. The pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 100 minutes, and the second pipe alone can empty it in 150 minutes. When both pipes are draining together, how long does it take them to empty the pool?

Explanation:

In the method I show below, the value 600,000 liters is never used. All that matters are the two values of 100 minutes and 150 minutes.

Pipe A drains the pool in 100 minutes. The rate it drains the pool is 1/100 of a pool per minute. If you multiply 1/100 by 100, then you'll represent 1 full job being done (that job being draining the pool).

Pipe B drains the pool in 150 minutes. Pipe B's rate is 1/150 of a job per minute.

In total, the combined rate is

1/100 + 1/150 = 3/300 + 2/300 = 5/300 = 1/60 of a pool per minute

This means it takes them 60 minutes to drain the pool assuming the two pipes work the most efficiently together (ie one pipe doesn't hinder the other). Since 60 minutes = 1 hour, it's much easier to say it takes 1 hour to drain the pool with both pipes working together.

We can get this same answer through solving the equation

1/x + 1/y = 1/z

for z. Use x = 100 and y = 150.

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step-by-step explanation: