SOLUTION: When two hoses are connected to a swimming pool, they can fill the pool in 4 hrs if both are open. If only the larger hose is open, it can fill the pool in 6 hrs less than the smal

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Question 1187411: When two hoses are connected to a swimming pool, they can fill the pool in 4 hrs if both are open. If only the larger hose is open, it can fill the pool in 6 hrs less than the smaller hose. How long will it take each hose to fill the pool?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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When two hoses are connected to a swimming pool, they can fill the pool in 4 hrs if both are open.
If only the larger hose is open, it can fill the pool in 6 hrs less than the smaller hose.
How long will it take each hose to fill the pool?
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Let x = hours to fill, for the smaller hose.

Then the time for the larger hose to fill the pool is  (x+4)  hours.


The equation for the combined rate of work is.

    1%2Fx + 1%2F%28x%2B6%29 = 1%2F4.    (1)


To solve it, multiply both sides by 4.  You will get

    4%2Fx + 4%2F%28x%2B6%29 = 1.     (2)


From this point, I just see the answer.  It is  x= 6 hours.


CHECK  equation (2).  Its left side is  4%2F6 + 4%2F%286%2B6%29 = 2%2F3 + 1%2F3 = 1   ! Correct !


Alternatively, you can reduce equation (2) to a quadratic equation
and solve it using the quadratic fotmula or factoring.


Knowing the answer will facilitate your job.

Solved and explained.