SOLUTION: ALICE CAN PAINT A ROOM IN 3 HOUR. PAT CAN PAINT A ROOM IN 2 HOURS. HOW LONG WILL IT TAKE THEM TO PAINT THE ROOM WORKING TOGETHER? PLEASE THIS IS DUE ON THURRDAY

Question 170696: ALICE CAN PAINT A ROOM IN 3 HOUR. PAT CAN PAINT A ROOM IN 2 HOURS. HOW LONG WILL IT TAKE THEM TO PAINT THE ROOM WORKING TOGETHER? PLEASE THIS IS DUE ON THURRDAY
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
ALICE CAN PAINT A ROOM IN 3 HOUR. PAT CAN PAINT A ROOM IN 2 HOURS. HOW LONG WILL IT TAKE THEM TO PAINT THE ROOM WORKING TOGETHER? PLEASE THIS IS DUE ON THURRDAY
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If you look at rooms per time, it's 3 hrs and 2 hrs. That's different denominators.
For this type of problem, you have to use the reciprocals.
Alice does 1/3 of a room per hour, Pat does 1/2 per hour.
Add those up: 1/3 + 1/2 = 5/6 rooms per hour.
Then invert that, for 6/5 hours per room
That's 1.2 hours, or 1 hour 12 minutes.

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