Question

You can paint a certain room in 7 hours. Your brother can do it in 6 hours. How long does it take the two of you working together?

Answer 1

the answer lies in knowing how long it takes for each of you to paint the room in one hour. you can paint 1 room in 7 hours; so in one hour 1/7 of the room is painted by you. bro can paint the room in 6 hours, so 1/6 of the room is painted by him in one hour. how much of the room can you and your bro paint in one hour:

1/7 + 1/6 = 13/42.

So in one hour you get 13/42 painted together; 2 hours is 26/42 painted 3 hours is 39/42 painted. So we are up to 3 hours.

Whats left? 3/42 = 1/14. What is 1/14th of an hour? That is 60/14 = 30/7 = 4 2/7

I would estimate 3 hours and 4 1/2 minutes...