An empty cistern can be filled by tap A in 1 hour 12 minutes and by tap B in 1 hour 48 minutes. Both taps are opened together. After how long is the cistern three-quarters full?

The taps take 72 and 108 minutes. Take the cistern as 216 units: A gives 3 units a minute, B gives 2, so together 5. Three-quarters is 162 units, and 162 ÷ 5 = 32.4 minutes. 43.2 minutes is the time to fill the cistern completely (216 ÷ 5). 54 minutes is three-quarters of tap A's own 72 minutes, leaving tap B out. 10.8 minutes is the time for the last quarter (54 ÷ 5), the part still to come rather than the part already in.