If it takes one person 3 hours to clean a room & another person 2 hours to clean how long will it take if they work together

Question

If it takes one person 3 hours to clean a room & another person 2 hours to clean how long will it take if they work together

Answer 1

Hi Judith.  

 

This is a "rate" problem.   If you can find how many rooms/hour person1 can clean, and how many rooms per hour person2 can clean, then you can just add these two rates.  

Person1 takes 3 hours to clean a room, or 1 room/3 hours = .3333 rooms/hour

Person2  takes 2 hours to clean a room, or 1 room/2 hours = 0.5 rooms/hour.

 

Together they can clean 0.33 + 0.5 = 0.83 rooms/hour

 

Do it in fractions and get 1/3 + 1/2 = 2/6 + 3/6 = 6/5 rooms/hour

 

Now flip this fraction and get 5/6 hours/room.   And 5/6 hour = 50 minutes.