Question 1188506: Two mechanics, Bonita Rich and Pamela Pearson, take 8 hours to rebuild an engine when they work together. If each worked alone, Bonita, the more experienced
mechanic, could complete the job 2 hours faster than Pamela. How long would it take each of them to rebuild the engine working alone?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! B takes x hours, so 1 hour is 1/x of the job
P takes x+2 hours so 1 hour is 1/(x+2) of the job
and (8/x)+(8/(x+2))=1 full job, the 8's coming from 8 hours they each worked
multiply by x(x+2)
and 8(x+2)+8(x)=x^2+2x
so 8x+16+8x=x^2+2x
x^2-14x-16=0
x=(1/2)(14+/- sqrt(196+64)); sqrt(260)=16.12
only positive root is x=15.06 hours for Bonita and 17.06 for Pamela
(8/15.06)=0.531 of the job
(8/17.06)=0.469 of the job
They add to 1
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