Two Taps Fill a Tank

1. 1Add the Times?The tempting answer is 4 + 6 = 10 hours. But two taps pour at once — together they must be FASTER than either alone, not slower.10 hours?
2. 2One Hour of Tap ACut the tank into 12 equal parts. In one hour tap A fills 3 of them: 3/12 = 1/4 of the tank.A per hour: 1/4 of the tank
3. 3One Hour of Tap BIn one hour tap B fills 2 parts: 2/12 = 1/6 of the tank. Slower tap, smaller share.B per hour: 1/6 of the tank
4. 4Both Taps, One HourTogether in one hour: 3 sky parts from A plus 2 green parts from B = 5 parts of 12. That is 1/4 + 1/6 of the tank every hour.Together per hour: 5/12 of the tank
5. 5Hour After HourAfter 2 full hours the joint tank holds 10 of 12 parts. Only 2 parts are missing.After 2 h: 10/12
6. 6The Last Part of an HourThe missing 2 parts are 2/5 of an hour's inflow: 24 minutes. Total time: 12 ÷ 5 = 2.4 hours = 2 hours 24 minutes.12 ÷ 5 = 2.4 h
7. 7Check and the Golden RuleCheck: 5 parts per hour × 2.4 hours = 12 parts — exactly one tank. ✓5 × 2.4 = 12 ✓

Change the numbers to test the engine with any sum & difference problem: