Question

It takes Sally 6 hours longer than Joan to paint a room. Working together, they can paint the room in 4 hours. How long would it take each person working individually to paint the room?

Answer 1

Assume sally has a rate of 1 room / x hours
Then Joan has a rate of 1 room / (x - 6) hours
and combined they have a rate of 1 room / 4 hours

so

1/x + 1/(x-6) = 1/4

solving that for x gives x = 12 or 2. 2 doesn't make sense because then Joan would be painting rooms in -4 hours. So Sally takes 12 hours and Joan takes 6 under normal circumstances.

Answer 2

Awesome. I just had Sally at (X+6) instead. Thank you.