SOLUTION: It takes Matt and Angie 4 hours to clean a house together. Separately it takes Matt two times as long as Angie, how long does it Angie to clean a house alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Matt and Angie 4 hours to clean a house together. Separately it takes Matt two times as long as Angie, how long does it Angie to clean a house alone?      Log On


   

Question 541504: It takes Matt and Angie 4 hours to clean a house together. Separately it takes Matt two times as long as Angie, how long does it Angie to clean a house alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = time for Angie to clean house alone
2t = time for Matt working alone
Add their rates working alone to get rate working together
( 1 house cleaned ) / ( 4 hours ) = rate working together
+1%2Ft+ = Angie's rate
+1%2F%282t%29+ = Matt's rate
+1%2Ft+%2B+1%2F%282t%29+=+1%2F4+
Multiply both sides by 4t
+4+%2B+2+=+t+
+t+=+6+
It takes Angie 6 hours to clean a house alone