Two taps fill a storage drum in 36 minutes and 45 minutes respectively when each works alone. Both are opened together, but the faster tap is shut off before the drum is full, and the drum fills in exactly 30 minutes. After how many minutes was the faster tap shut off?

Take the drum as 180 units: the faster tap gives 5 units a minute, the slower 4. The slower tap runs the whole 30 minutes and supplies 120 units, so the faster tap must supply the other 60 units at 5 a minute — it ran for 12 minutes. 18 minutes is how long the faster tap stayed shut (30 − 12), not the moment it was closed. 7.5 minutes solves the problem with the roles swapped, shutting the slower tap instead. 6 minutes comes from 36 − 30, subtracting the fill time from the faster tap's solo time, which mixes times with quantities.