Question 694392
Let x=amount of time it takes both working together to paint the house
So, working together, they paint at the rate of 1/x house per hour
The painter paints at the rate of 1/6 house per hour
The apprentice paints at the rate of 1/9 house per hour
So, working together, they paint at the rate of 1/6 + 1/9 =3/18 +2/18=5/18 house per hour
Our equation to solve, then, is:
5/18=1/x multiply each side by 18x or cross-multiply
5x=18
x=18/5 hours=3 3/5 hours---time it takes both working together
CK
In 18/5 hours, the painter paints (18/5)(1/6)=3/5 of the house
In 18/5 hours the apprentice paints (18/5)(1/9) =2/5 of the house
3/5 + 2/5 =5/5 which is all of the house :)
Hope this helps----ptaylor