Question 5692: A swimming pool can be filled in 6 h and requires 9 h to drain. If the drain was accidentally left open for 6 h while the pool was being filled, how long did filling the pool require?
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! This problem requires two parts. Part I would be to find the amount of the pool filled during the first six hours while the pool was left to be able to drain. Part II would be to figure out how long it would take the filling pump to fill the remaining volume of the pool, assuming that they closed the drain.
Part Zero. This is a r*t = w type problem. From reading the problem, it might not be obvious how you find the rate, work and time, and that the values 6 hrs and 9 hrs look very tempting to plug into the t. Actually, if the pool took 6 hours to fill, that took 6 hours to do 1 job. So, using r*t = w, r * 6 = 1. Solving for r will get you the pump's filling rate, which is 1/6 of the pool per hour. Likewise, for the drainage rate, it takes 9 hours to drain it. In other words, 9 hours to do 1 job. So drain * 9 = 1, then drain = 1/9.
Part I. The first six hours. Obviously, if it takes the pump alone to fill the pool in the first six hours, we're done. But the drain was left open. Obviously, if it drained in the first six hours, the pump did not fill the pool.
 <---- So only 1/3 of the pool is actually filled in the first 6 hours.
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