SOLUTION: It takes Sal 5 hours to paint a house. It takes Pal 3 hours to paint the same house. How long will it take to paint the house if both of them work together?

Question 381055: It takes Sal 5 hours to paint a house. It takes Pal 3 hours to paint the same house. How long will it take to paint the house if both of them work together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
The fast way is 5*3/(5+3)=15/8=1 7/8 hour but here is another way:
Let x=amount of time it takes both working together to paint the house
Then working together, they paint at the rate of 1/x house per hour
Sal works at the rate of 1/5 house per hour
Pal works at the rate of 1/3 house per hour
So, together they work at the rate of 1/5 + 1/3 house per hour
Now our equation to solve is:
1/5 + 1/3 = 1/x multiply each term by 15x
3x+5x=15
8x=15
x=15/8 hr
CK
In 15/8 hour, Sal paints (1/5)(15/8)=3/8 of the house
In 15/8 hour, Pal paints (1/3)(15/8)=5/8 of the house
3/8 + 5/8 =1 (house that is)
Hope this helps ---ptaylor
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