Three taps A, B and C can fill a tank in 8, 10 and 12 hours respectively. Tap A is open all the time, but taps B and C are open for one hour each alternately. How long will it take for the tank to be full?

The tank fills in 4 16/27 hours.

Rates are A = 1/8, B = 1/10, C = 1/12 per hour; A stays open with B and C alternating.

Hour 1 (A+B) = 9/40 and hour 2 (A+C) = 5/24, so a 2-hour block = 13/30.

After 4 hours two blocks fill 26/30 = 13/15, leaving 2/15.

Hour 5 runs A+B = 9/40; time for 2/15 = (2/15)/(9/40) = 16/27, total 4 16/27 hours.