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.