Question: A dam can be lowered by 4 meters using spillway A in 4 hours, or by spillway B in 6 hours (also lowering the water level by 4 meters).
(a) Without finding the correct answer, why does it not take 5 hours for the dam to be lowered by 4 meters with both spillways open? (An assumption we will make in this problem is that the spillways don't intefere with each other.) How do you know it can't take less than 2 hours?
(b) If the time taken to lower the dam by 4 meters if both spillways are used together isT, find an equation that determinesT. (Remark: If the rate of water leaving spillway A is a certain amount per minute, say, and the amount leaving spillway B is a certain amount per minute, then the combined rate from spillway A and B will be the sum of these rates.)
(c) Solve the previous equation for T.