Kelly took 4 hours to paint a room. Richard took 8 hours to paint an identical room. If both of them worked together, how long would they take to paint the room?

Here's an easy way to do this

1/4 + 1/8 =

2/8 + 1/8 =

3/8

Take the reciprocal of this fraction = 8/3 = hrs to paint the room if they work together = 2 + 2/3 hrs =

2hrs 40 min

Kelly painting rate = 1 room / 4hours = 1/4

Richard painting rate = 1 room / 8hours = 1/8

Remember job / rate = time ( or distance / rate = time)

Now combine the rates

1 room / ( 1/4 + 1/8) = 1 / (2/8 + 1/8) = 1/(3/8) = 8/3 hour 2 2/3 hour for both of them working