Ok. I am helping my cousin do word problems but I am having trouble explaining the method or principles behind why I set up the equations the way I do. 1. The problem statement, all variables and given/known data Terence and Mao are mowing a lawn together. Terence can mow 3 of these lawns in 5 hours. Matt can mow 2 of these lawns in 3 hours. Assuming they work independently, how long does i take them to mow the lawn together? I let T = the time it takes in hours to mow the lawn with both people, what we are solving for. I let A = Area of the lawn. R_T = 3 lawns / 5 hrs = 3A / 5 hrs R_M = 2A / 3 hrs 2. Relevant equations I set up the equation: A = (R_T + R_M)*T and solve for T. So A = (3/5A + 2/3A)*T = (19/15 * T)A --> T = 15/19 hrs 3. The attempt at a solution I am having trouble explaining why we set up the rates as lawns per hour instead of hours per lawn. I know it will yield the wrong answer if we try to solve T = (R_T + R_M)*A where our rates are in hours per lawn because it doesn't really make sense to add the rates that way. Of course I can show 3/4 + 1/2 != 4/3 + 2/1 and that when we add speeds we add them time on the bottom distance on the top, but is there a reason behind this? Is there a theoretical or generalized reason why we do this? In many other word problems it is OK to invert the ratios or rates.. I suspect we run into trouble here and have to do it the specific, right way (time on the denominator) because the area being mowed by Terence depends on the are being mowed by Mao. Can someone give me any insight? If this is more suited for the math general forum please move it there.