A swimming pool can be filled in 13 hours if water enters through a pipe alone, or in 21 hours if water enters through a hose alone. If water is entering through both the pipe and the hose, how long will it take to fill the pool?
It will take hours to fill the pool if water is entering through both the pipe and the hose. (Simplify your answer. Type an integer, fraction, or mixed number.)
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(1) Time Remaining: 00:26:19
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Step 1 ：The problem is asking for the time it takes to fill the pool when both the pipe and the hose are used simultaneously. This is a problem of rates. The rate of the pipe is 1 pool per 13 hours and the rate of the hose is 1 pool per 21 hours. The combined rate is the sum of the individual rates. The time it takes to fill the pool is the reciprocal of the combined rate.

Step 2 ：First, calculate the rate of the pipe, which is \(\frac{1}{13}\) pools per hour, approximately 0.07692307692307693 pools per hour.

Step 3 ：Next, calculate the rate of the hose, which is \(\frac{1}{21}\) pools per hour, approximately 0.047619047619047616 pools per hour.

Step 4 ：Then, calculate the combined rate by adding the rate of the pipe and the hose, which is approximately 0.12454212454212454 pools per hour.

Step 5 ：Finally, calculate the time it takes to fill the pool by taking the reciprocal of the combined rate, which is approximately 8.029411764705882 hours.

Step 6 ：Final Answer: The time it will take to fill the pool if water is entering through both the pipe and the hose is approximately \(\boxed{8.03}\) hours.