SOLUTION: tim can paint a house in 20 hours and his friend can paint a house in 30 hours. how long would it take them working together?

Question 629240: tim can paint a house in 20 hours and his friend can paint a house in 30 hours. how long would it take them working together?
Found 2 solutions by richwmiller, MonicaStitt:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x/20+x/30=1
multiply both sides by 60
3x+2x=60
5x=60
x=12
12 hours together.
check
12/20+12/30=1
3/5+2/5=1
1=1
ok
Answer by MonicaStitt(2) (Show Source): You can put this solution on YOUR website!
What is the given rate of work of each person working alone?
1: Tim would work 20 hours to paint one house alone.
h = number of houses; w = actual work hours; 20 is the hours per house
20 times h equals w or

2: Friend of Tim, would work 30 hours to paint one house alone.
h = number of houses; w = actual work hours; 30 is the hours per house
30 times h equals w or

3: 20h = w and 30h = w .......... w square = 20h * 30h = 600
(h = 1, & the square of h = 1)
Solve: actual work hours -combined- (that is two people). Divide by the number of workers, i.e. divide by 2.

Answer: Working together the house is done in 12 and a quarter hours; 12 hours 15 minutes.
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