SOLUTION: A hose can fill a swimming pool in 12 hours. Another hose needs 2 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

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Question 902819: A hose can fill a swimming pool in 12 hours. Another hose needs 2 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
RATES in POOL per HOUR
hose1, 1%2F12
hose2, 1%2F%28x%2B2%29
hose1&2, 1%2Fx

Careful reading the description will give the right understanding for transcribing the rates.

The rate for the two hoses combined is the sum of the rates of the two hoses. The equation representing this is highlight_green%281%2F12%2B1%2F%28x%2B2%29=1%2Fx%29.
LCD is 12x%28x%2B2%29, so ....

12x%28x%2B2%29%281%2F12%2B1%2F%28x%2B2%29%29=12x%28x%2B2%29%2Fx
x%28x%2B2%29%2B12x=12%28x%2B2%29
x%5E2%2B2x%2B12x=12x%2B24
x%5E2%2B2x=24
x%5E2%2B2x-24=0
FACTORABLE
%28x-4%29%28x%2B6%29=0
highlight%28x=4%29-----hose 1 and 2 together fill the pool in 4 hours.

Hose2 needs x%2B2=4%2B2=highlight%286%29------ 6 hours to fill the pool.