A water tanker is filled by two nozzles that are never run together — one is used first and the other takes over in succession. The wide nozzle alone would fill the tanker in 24 minutes and the narrow one in 40 minutes. The wide nozzle runs first for 9 minutes and the narrow one then completes the filling. For how many minutes does the narrow nozzle run?

Take the tanker as 120 units: the wide nozzle gives 5 units a minute, the narrow one 3. Nine minutes of the wide nozzle put in 45 units, leaving 75, and 75 ÷ 3 = 25 minutes of the narrow nozzle. 34 minutes is the total filling time, 9 + 25, not the narrow nozzle's own stretch. 31 minutes subtracts the 9 minutes from the narrow nozzle's solo 40, which has nothing to do with the part left. 15 minutes multiplies 40 by the fraction already filled (45/120 = 3/8) instead of by the 5/8 still to go.