SOLUTION: Pat and Mike working together can assemble a bookcase in 8 minutes. It takes Mike, working by himself, 12 minutes longer than it takes Pat working by himself to assemble the bookca

Question 1045657: Pat and Mike working together can assemble a bookcase in 8 minutes. It takes Mike, working by himself, 12 minutes longer than it takes Pat working by himself to assemble the bookcase. How long does it take each, working alone, to do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Pat and Mike working together can assemble a bookcase in 8 minutes.
It takes Mike, working by himself, 12 minutes longer than it takes Pat working by himself to assemble the bookcase.
How long does it take each, working alone, to do the job?
:
let p = time for Pat to do the job alone
then
(p+12) = time for Mile to do it
:
let the completed job = 1, (Each does a fraction of the job, the two fractions add up to 1)
+ = 1
multiply the equation by p(p+12)
p(p+12)* + p(p+12)* = 1p(p+12)
Cancel the denominators
8(p+12) + 8p = p^2 + 12p
8p + 96 + 8p = p^2 + 12p
16p + 96 = p^2 + 12p
Form a quadratic equation on the right
0 = p^2 + 12p - 16p - 96
p^2 - 4p - 96 = 0
Factors to
(p-12)(p+8) = 0
the positive solution
p = 12 min for Pat to do the job
then
12 + 12 = 24 min for Mike to do it
:
:
see if that check s out
+ = 1
+ = 1
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