If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Sally can complete one house in four hours:

##(S_(hour))/(house) = 4##

##(house)/(S_(hour))= 1/4##

John can complete one house in six hours:

##(J_(hour))/(house) = 6##

##(house)/(J_(hour))= 1/6##

We want to know how many hours together, ##T_(hour)##, it takes John and Sally to complete one house:

##(house)/(T_(hour)) = (house)/(S_(hour)) + (house)/(J_(hour))##

##1/(T_(hour)) = 1/4 + 1/6##

Multiply both sides by ##T_(hour)##

##1 = (1/4 + 1/6)*T_(hour)##

##1 = 0.41dot6*T_(hour)##

Divide both sides by ##0.41dot6##

##T_(hour) = 1/(0.41dot6)##

##T_(hour) = 2.4##

It would take Sally and John ##2.4## hours (or ##2## hours and ##24## minutes) to complete one house together.