Question 708995
A hose can fill a swimming pool in 6 hours.
 Another hose needs 3 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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Let's do it this way
Let x = time required when the two hose work together
then
(x+3) = time required by the 2nd hose 
let the full pool = 1
:
{{{x/6}}} + {{{x/((x+3))}}} = 1
multiply by 6(x+3)
x(x+3) + 6x = 6(x+3)
x^2 + 3x + 6x = 6x + 18
x^2 + 3x + 6x - 6x - 18 = 0
x^2 + 3x - 18 = 0
Factors to
(x+6)(x-3) = 0
the positive solution
x = 3 hrs when working together
then
6 hrs using just the 2nd hose

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you can confirm this in the original shared work equation