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Mike and Gerry can finish building a doghouse in 4 hours. It would take mike 6 more hours than Gerry to finish the job alone. How long would it take each boy to finish the job if each works alone?
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x = time it takes Gerry to do the job alone
x+6 = time it takes Mike to do the job alone (he takes 6 hrs longer than Gerry)
1/(Gerry's time) + 1/(Mike's time) = 1/(combined time)
1/x + 1/(x+6) = 1/4
4x(x+6)[1/x + 1/(x+6)] = 4x(x+6)*1/4 See Note below
4x(x+6)[1/x] + 4x(x+6)[1/(x+6)] = 4x(x+6)*1/4
4(x+6) + 4x = x(x+6)
4x+24 + 4x = x^2+6x
24 + 8x = x^2+6x
0 = x^2+6x-8x-24
0 = x^2-2x-24
x^2-2x-24 = 0
(x-6)(x+4) = 0
x-6=0 or x+4 = 0
x=6 or x = -4
Note: Multiply both sides by the LCD 4x(x+6) to clear out the fractions
The possible solution of x = -4 makes no sense at all since time values can only be positive or 0.
So toss that possible solution.
The only solution is x = 6
x = 6
x+6 = 6+6 = 12
So this means
it takes Gerry 6 hours to do the job alone
and
it takes Mike 12 hours to do the job alone
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