SOLUTION: Jill builds a dog house in 4 hours. Todd builds the same type of dog house in 6 hours. How long will it take them to build a house together?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Jill builds a dog house in 4 hours. Todd builds the same type of dog house in 6 hours. How long will it take them to build a house together?      Log On


   

Question 198837: Jill builds a dog house in 4 hours. Todd builds the same type of dog house in 6 hours. How long will it take them to build a house together?
Found 2 solutions by user_dude2008, josmiceli:
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
t(1/4+1/6)=1


t(3/12+2/12)=1

t(5/12)=1

t=12/5

t=2.4

Answer: takes 2.4 hours (2 hrs and 24 min) working together

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
Jill's rate of building: (1 dog house) / (4 hours)
Todd's rate of building: (1 dog house) / (6 hours)
Let t = time to build 1 dog house working together
Add their rates to get rate with both working together
1%2F4+%2B+1%2F6+=+1%2Ft
3%2F12+%2B+2%2F12+=+1%2Ft
Multiply both sides by 12t
3t+%2B+2t+=+12
5t+=+12
t+=+2.4
It will take them 2.4 hours working together