Jan and Pete are home decorators. Jan can paint 3 rooms in 2 hours. Pete can paint 2 rooms in 3 hours. If they work together, about how many hours will it take Jan and Pete to paint 6 rooms?

Answer 1

Jan's rate = 3/2 rooms/hr
Pete's rate = 2/3 rooms/hr
combined rate = 3/2 + 2/3 rooms/hr = 16/6 rooms/hr

time to do 1 room at combined rate = 1/(16/6) hrs = 6/16 or 3/8 hrs
so to do 6 rooms would take 6(3/8) hours
= 9/4 hrs or 2 hours and 15 minutes

Answer 2

Jan's rate = 3/2 rooms/hr
Pete's rate = 2/3 rooms/hr
combined rate = 3/2 + 2/3 rooms/hr = 16/6 rooms/hr

time to do 1 room at combined rate = 1/(16/6) hrs = 6/16 or 3/8 hrs
so to do 6 rooms would take 6(3/8) hours
so = 9/4 hrs or 2 hours and 15 minutes