FILE No.72Unsolved
A tank has Tap A and Tap B. Tap A alone fills the empty tank in 3 hours, and Tap B alone in 6 hours.
One night, the culprit opened both taps at once and let the tank fill. There is no drain and the flow is steady.
How many hours does it take to fill the empty tank with both taps open?
If you get stuck, open the hints one at a time, in order.
Treat the whole tank as 1 and ask how much each tap fills in one hour.
Add the two hourly amounts.
Divide the whole tank by that amount.
How many hours does it take to fill the empty tank with both taps open?
Choose the answer closest to the truth.
2 hours
The answer is: 2 hours.
Call the whole tank 1. Tap A fills 1/3 per hour and Tap B 1/6 per hour. Together: 1/3 + 1/6 = 1/2 per hour. So filling 1 takes 1 / (1/2) = 2 hours.
People average 3 and 6 and answer 4.5 hours.
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