Questions: A swimming pool holds 480,000 liters of water. The pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 120 minutes, and the second pipe alone can empty it in 240 minutes. When both pipes are draining together, how long does it take them to empty the pool? minutes

A swimming pool holds 480,000 liters of water. The pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 120 minutes, and the second pipe alone can empty it in 240 minutes. When both pipes are draining together, how long does it take them to empty the pool?
minutes

Transcript text: A swimming pool holds 480,000 liters of water. The pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 120 minutes, and the second pipe alone can empty it in 240 minutes. When both pipes are draining together, how long does it take them to empty the pool? $\square$ minutes

Solution

Solution Steps

Step 1: Calculate the rate at which each pipe can empty the pool

The rate for the first pipe is $\frac1{T_1} = \frac1{120}$ pools per minute. The rate for the second pipe is $\frac1{T_2} = \frac1{240}$ pools per minute.

Step 2: Calculate the combined rate at which both pipes can empty the pool together

The combined rate is $\frac1{T_1} + \frac1{T_2} = \frac1{120} + \frac1{240} = 0.0125$ pools per minute.

Step 3: Calculate the time required for both pipes to empty the pool together

The time $T$ required for both pipes to empty the pool together is $\frac1{combined\_rate} = \frac1{0.0125} = 80$ minutes.

Final Answer: The time required for both pipes to empty the pool of volume 480000 liters together is 80 minutes.

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