SOLUTION: Ellie and Ruth make plans to paint the house. Ellie can paint it in 10 hours. Ruth says she can paint it in 6 hours. How long will it take them to paint the house together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Ellie and Ruth make plans to paint the house. Ellie can paint it in 10 hours. Ruth says she can paint it in 6 hours. How long will it take them to paint the house together?       Log On


   

Question 71603: Ellie and Ruth make plans to paint the house. Ellie can paint it in 10 hours. Ruth says she can paint it in 6 hours. How long will it take them to paint the house together?

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= amount of time it takes them to paint the house together
Now We know that Ellie can paint 1/10 of the house per hour
And Ruth can paint 1/6 of the house per hour
Together they can paint 1/10+1/6 of the house per hour
1/10+1/6=3/30+5/30=8/30=4/15 of the house per hour
Ruth and Ellie can paint 4/15 of the house per hour

Now, if they can paint 4/15 of the house per hour, how many hours will it take them to paint all the house? So our equation to solve is:

%284%2F15%29%28x%29=%2815%2F15%29 multiply both sides by 15
(Note: 15%2F15 represents all of the house)
4x=15 divide both sides by 4
x=3.75hours
Hope this helps----ptaylor