SOLUTION: Two men painted a room in 3 hours. How long would it take each of them while working alone to paint the room if the faster one can do it in 2 1/2 hours less than the other one?
Algebra ->
Rate-of-work-word-problems
-> SOLUTION: Two men painted a room in 3 hours. How long would it take each of them while working alone to paint the room if the faster one can do it in 2 1/2 hours less than the other one?
Log On
Question 406050: Two men painted a room in 3 hours. How long would it take each of them while working alone to paint the room if the faster one can do it in 2 1/2 hours less than the other one? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Two men painted a room in 3 hours. How long would it take each of them while working alone to paint the room if the faster one can do it in 2 1/2 hours less than the other one?
.
Let x = time it takes slower painter
the
x-2.5 = time it takes faster painter
.
3(1/x + 1/(x-2.5)) = 1
multiplying both sides by x(x-2.5):
3((x-2.5) + x) = x(x-2.5)
3(2x-2.5) = x(x-2.5)
6x-7.5 = x^2-2.5x
-7.5 = x^2-8.5x
0 = x^2-8.5x+7.5
0 = (x-7.5)(x-1)
x = {1, 7.5}
we can throw out 1 leaving:
x = 7.5 hours (slower painter)
.
faster painter:
x-2.5 = 7.5-2.5 = 5 hours
