Bob and sarah need to paint a fence. bob can paint the fence in 4 hours and sarah can paint the fence in 2.5 hours. if they work together, how long will it take them to paint the fence?

If Bob can paint the fence in 4 hours, then in 1 hour he gets 1/4 of the fence painted.  If Sarah can paint the fence in 2.5 hours, then she gets 2/5 of the fence painted in one hour (1/2.5 = 2/5).  We add those amounts together and set them equal to 1/x, x being the the total time it will take them to paint the whole fence.  1/4 + 2/5 = 1/x.  Find a common denominator first, then add the left side together.  5/20 + 8/20 = 1/x.  13/20 = 1/x.  Cross-multiply to get 13x = 20 and x = 1.54 hours, just a bit over an hour and a half.