SOLUTION: please help my friend's homework hehe thankyou Mike and gerry can finish building a doghouse in 4 hours. It would take mike 6 more hours that gerry to finish the job working alone

Question 1197454: please help my friend's homework hehe thankyou
Mike and gerry can finish building a doghouse in 4 hours. It would take mike 6 more hours that gerry to finish the job working alone. How long would it take each boy if each works alone?
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Mike and gerry can finish building a doghouse in 4 hours.
It would take mike 6 more hours THAN gerry to finish the job working alone.
How long would it take each boy if each works alone?
~~~~~~~~~~~~~~

Let    be the number of hours for gerry to cover the roof, working alone.
If Mike works alone, he can complete this job in    hours.
Thus, in one single day Mike covers    part of the roof area, while gerry covers    part of the roof area.
Working together, Mike and gerry make    of the whole work in each single day.
Since they can cover the entire roof in 6 hours working together, the equation for the unknown value    is as follows:

        .

To simplify this equation, multiply both sides by , then transfer all terms
from the right side to the left with the opposite signs, collect the common terms
and adjust the signs. In this way you get

        ,
        ,
        ,
        ,

You get the quadratic equation. It is factorable

        (x-6)*(x+4) = 0

The equation has two roots:    and .
The second root    makes no sense and we decline it.
So, the potentially correct solution is : gerry covers the roof in 6 hours working alone.
Hence, Mike can complete the job in 6+6 = 12 hours.

Let us check it.

Since = = , this solution is correct.

Answer. gerry can finish the job in 6 hours working alone. Mike can complete the job in 12 hours.

Solved.

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