two hoses used to fill maddies neighborhood swimming pool .one hose can fill in 10 hrs and second hose can fill the pool in 12 hrs, the pool drain can empty the pool in 8hrs, if the two hoses are working together and the pool drain open by mistake, how long will it take to fill the pool?
Answers
Answer:
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Step-by-step explanation:
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Given: One hose can fill in 10 hrs and the second hose can fill the pool in 12 hrs. The pool drain can empty the pool in 8hrs.
To find: Time taken to fill the pool if all the three are working together
Solution: The time taken by the first hose to fill the pool = 10 hrs.
Therefore, the work done by the first hose in 1 hr = 1/10.
The time taken by the second hose to fill the pool = 12 hrs.
Therefore, the work done by the second hose in 1 hr = 1/12.
The time taken by the pool drain to empty the pool = 8 hrs.
Therefore, the work done by the pool drain in 1 hr = 1/8.
As such, the work done by the three together in 1 hr
= 1/10 + 1/12 - 1/8
= (12 + 10 - 15)/120
= 7/120
Hence, the time taken to fill the pool if the two hoses are working together and the pool drain is opened by mistake = 120/7 = 17.1 hrs = 17 hrs (approx.)
Answer: 17 hrs