Bill and Peter can paint a 75 ft wall together in 7 hours. because Bill has more experience he can paint alone in two hours quicker than Peter. how long can it take Peter to paint the wall alone? round to the nearest minute.
+128474 Let the portion of the wall that Bill can paint in one hour be 1/x = his rate where x is the number of hours that Bill takes to paint the wall by himself
Let the portion of the wall that Peter can paint in one hour = 1/ ( x + 2) = his rate where x + 2 is the number of hours that Peter takes to paint the wall by himself
And
Bill's rate * 7hours + Peter's rate * 7 hours = 1 whole job done.....so...
1/x * 7 + 1/(x + 2) * 7 = 1
7/x + 7/(x + 2) = 1
7 ( x + 2) + 7x
______________ = 1
x ( x + 2)
14x + 14 = x ( x + 2)
14x + 14 = x^2 + 2x rearrange as
x^2 - 12x - 14 = 0 complete the square on x
x^2 -12x + 36 = 14 + 36
(x - 6)^2 = 50 take the positive root
x - 6 = sqrt (50)
x = sqrt (50 ) + 6
x + 2 = sqrt (50 ) + 8 ≈ 15.07 hrs = Peter's time = 15 + .07 *60 ≈ 15 hrs 4 min
