SOLUTION: It takes Lucy 15 minutes longer to clean her garage alone than it takes her brother Billy. Together they can clean the garage in 4 minutes. If Lucy were cleaning the garage alone

Question 168173: It takes Lucy 15 minutes longer to clean her garage alone than it takes her brother Billy. Together they can clean the garage in 4 minutes. If Lucy were cleaning the garage alone, how long would it take her to complete the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
:
It takes Lucy 15 minutes longer to clean her garage alone than it takes her brother Billy.
:
Together they can clean the garage in 4 minutes.
:
If Lucy were cleaning the garage alone, how long would it take her to complete the job?
:
Let x = L's time (in minutes) working alone
then
(x-15) = B's time working alone
:
Let the completed job = 1
:
+ = 1
:
Multiply equation by x(x-15) to get rid of the denominators, results:
4x + 4(x-15) = x(x-15)
:
4x + 4x - 60 = x^2 - 15x
:
8x - 60 = x^2 - 15x
:
Arrange as a quadratic equation:
x^2 - 15x - 8x + 60 = 0
:
x^2 - 23x + 60 = 0
Factor this to:
(x - 3)(x - 20)
:
x = 3 does not make sense
:
x = 20 min, L's time working alone.
:
:
Check solution; B's time would be 20 - 15 = 5 min
+ = 1
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