Alex frosts 1 wedding cake in 6 hr. It takes Bob 7 hr to frost a wedding cake. If they work together, how much time does it take to frost one cake?

Alex frosts 1 cake / 6 hours, and Bob frosts 1 cake / 7 hours. So every hour, Alex frosts 1/6 of a cake, and Bob frosts 1/7 of a cake. Together, every hour they frost 1/6 + 1/7 = 13/42 of a cake. (13/42 cakes/hour)(42/13 hours) = 1 cake.