A certail pool of 12000 liters has two vaults; A to fill the pool and B to pour out. The rate of the filling vault is 500 liters per hour; that of B is 100 lph. The vaults start to work simultaneously. When the pool is half full, the vault A stops to work for 5 hours and 12 minutes and then resumes its working. The vault B works without interruptions. How lond will it take to fill the pool completely?
First of all, it doesn't make any difference when A shuts down. so long as there are at least 520 liters in the pool, so you don't have to figure out exactly when the pool is half full. The only thing that is important is that B is draining the pool by itself for 5.2 hours. Hence B dumps 520 liters that the two working together have to make up. So the problem is simply the combined rate of 400 working for some time to fill 12520 liters + 5.2 hours. The answer is 31.3 hours + the 5.2 hours = 36.5 hours.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993