SOLUTION: Homer and Mike were replacing the boards on Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 5 hours until Homer had to go hom
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Question 1174769: Homer and Mike were replacing the boards on Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 5 hours until Homer had to go home. Mike finished the job working by himself in an additional 2 hours. How long would it have taken Homer to fix the deck himself?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Homer's rate of work = of the job per hour
Mike's rate of work = of the job per hour
Rate of work working together = + of the job per hour
Simplify:
+
Rate of work working together = of the job per hour
After working five hours together, calculate the amount of the job that was completed:
Therefore, the amount of the job that is left to be completed is:
Mike finishes the job in two hours. This means Mike's rate of work per hour is:
*
So, Mike's rate of work is of the job per hour.
From earlier, we know that Mike's rate of work is also of the job per hour. Therefore:
=
Solve for x.
Cross-multiply:
=
=
=
Use the quadratic formula to solve for x:
x = = 0.40
x = = 12.60
There are two solutions. Because Mike's rate of work is of the job per hour, the first solution, x = 0.40, would make Mike's rate of work . Since this is a negative rate of work, this is impossible.
Therefore, we are left with x = 12.60
We are looking how long it would have taken Homer to fix the deck working alone. Homer's rate of work is of the job per hour. Plugging in x = 12.60, this means Homer's rate of work is of the job per hour. This means it would have taken Homer 12.60 hours to fix the deck working alone.
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