SOLUTION: If your friend take 5 hours longer to clean a house and together it takes 6 hours. How long will it take you to clean the house?

Question 168151: If your friend take 5 hours longer to clean a house and together it takes 6 hours. How long will it take you to clean the house?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If your friend take 5 hours longer to clean a house and together it takes 6 hours.
How long will it take you to clean the house?
:
Let t = time required for you to clean the house
then
(t+5) = your friends time to do the same
:
Let the cleaned house = 1
:
+ = 1
:
Multiply equation by t(t+5) to get rid of the denominator, results:
6(t+5) = 6t = t(t+5)
:
6t + 30 + 6t = t^2 + 5t
:
12t + 30 = t^2 + 5t
arrange as a quadratic equation:
t^2 + 5t - 12t - 30 = 0
:
t^2 - 7t - 30 = 0
factors to
(t - 10)(t + 3) = 0
The positive solution is what we want here:
t = 10 hrs you working alone
:
:
Check: (Friends time: 10 + 5 = 15 hrs
+ = 1
+ = 1
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