SOLUTION: Working together, Butch and Manny can paint a wall in 3 hours. Working alone, Butch can do the job in 5 hours. How long will it take Manny to do the job alone?

Question 534996: Working together, Butch and Manny can paint a wall in 3 hours. Working alone, Butch can do the job in 5 hours. How long will it take Manny to do the job alone?

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Manny to do the job alone
Working alone Manny paints at the rate of 1/x wall per hour
Working together Butch and Manny paints at the rate of 1/3 wall per hour
Working alone Butch paints at the rate of 1/5 wall per hour
Sooooo, our equation to solve is:
1/x + 1/5=1/3 multiply each term by 15x
15+3x=5x
2x=15
x=7.5 hrs------amount of time it takes Manny to do the job alone
CK
In 3 hrs Manny paints 3/(7.5) of the wall
In 3 hrs, Butch paints 3/5 of the wall
3/(7.5)+3/5 should equal 1 (1 wall that is)
6/15+9/15=15/15=1
1=1
Hope this helps---ptaylor
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