Pretest

There’s an outdoor swimming pool on campus. To keep it clean, the water is changed each weekend. Two valves are used to control the flow of water. When valve A opens, water will be filled into the pool at the speed a m3 /h. When valve B opens, water will be drained from the pool at the speed b m3 /h (b is smaller than a) The volume of this pool is c m3

1) Usually, in order to fully change the pool’s water, Jim, the operator guy, will drain out the water before he started to fill in new water. If one day, Jim occasionally forgot to turn off valve B before he started to fill up the empty pool, how many more hours will it cost to fill this pool to full when compared to usual?

2) Assume the same situation in 1): two valves are both open, but now considering that during the process, the water evaporates quickly (e m3 /h ) in a sunny afternoon, then how many more hours will it cost to fill this pool to full when compared to usual?

3) Assume the same situation in 1), two valves are both open, but it happened to a thunder storm 1 h after Jim started to fill the pool. He then shut down the electricity (both valve stopped working during this period of time, no water fill-in and drain out). The storm lasted for ½ hour. During the storm, the rain filled in the pool is d m3.( d<c) After the thunder storm, Jim turned on the electricity so that both valves started to work as before. What is the time difference (hours) to fill the pool to full between this case and the usual? (hint, it may be more or less than usual)

4) Assume the same situation In 3), but now Jim realized that he made the mistake to let both valves open 2 hours after he restarted the electricity. He turned off B immediately and leave valve A on. What is the time difference (hours) to fill the pool to full between this case and the usual?

1+2+0.5+[c- 3(a-b)-d]/a – c/a or c/a-3.5- [c- 3(a-b)-d]/a