If Richard can paint their living room in 4 hours, and Vanessa can paint the same living room in 5 hours, then how long will it take them to paint the living room working together?

2 hrs 13 mins

Step-by-step explanation:

If Richard can paint the living room in 4 hrs, then in 1 hour he can paint 1/4 of the living.

If Vanessa can paint the living room in 5 hours, then in one hour, she can paint 1/5 of the living room.

In one hour Richard and Vanessa can paint 1/4 + 1/5 = 1/y

y is the number of hours it will take both Richard and Vanessa to paint the living room. 1/y is how much of the house they can paint in one hour.

1/4 + 1/5 = 1/y

(5 + 4) / 20. (find the LCM)

9/20 = 1/y

9y = 20

y = 20/9

y = 2.22hrs

y = 2 hrs 13 mins