Nancy can paint a house twice as fast as Terry can They year

Nancy can paint a house twice as fast as Terry can. They year they worked together it took them 7 days. How long would it take each to paint the house alone?

Solution

Let x=amount of time it takes Nancy to paint a house
Then 2x= amount of time it takes Terry to paint a house
Now Nancy can paint at the rate of 1/x houses per day
Terry can paint at the rate of 1/2x houses per day
Together they can paint at the rate of 1/7 house per day. So our equation to solve is:
(1/x)+(1/2x)=1/7 multiply each term by 14x
14+7=2x collect like terms
21=2x divide both sides by 2
x=10.5 days-------Amount of time it takes Nancy to paint a house
2x=2*10.5=21 days----Amount of time it takes Terry to paint a house
CK
(1/10.5)+1/21=1/7 multiply each term by 21
2+1=3
3=3
Also
10.5*2=21
21=21

Hope this helps