SOLUTION: If a painter can paint a house in 6 hours and his apprentice can paint the same sized house in 9 hours, how long will it take for them to paint a house if they worked together?"

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If a painter can paint a house in 6 hours and his apprentice can paint the same sized house in 9 hours, how long will it take for them to paint a house if they worked together?"       Log On


   



Question 694392: If a painter can paint a house in 6 hours and his apprentice can paint the same sized house in 9 hours, how long will it take for them to paint a house if they worked together?"

Found 3 solutions by jim_thompson5910, checkley79, ptaylor:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1/6 + 1/9 = 1/t

3/18 + 2/18 = 1/t

5/18 = 1/t

5t = 18

t = 18/5

So it will take them 18/5 hours, or 3 and 3/5 hours (or 3.6 hours = 3 hours and 36 minutes) if they work together.

Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
1/6+1/9=1/x
find the lcd (18)
(3+2)/18=1/x
5/18=1/x cross multiply.
5x=18
x=18/5
x=3.6 hours.

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
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