DAY 425

PASS THE SOAP
Credit: GAMES Magazine - Mar. 1983
Clara Hall

The cold-water tap fills our tub in 6 minutes 40 seconds, the hot water tap in 8 minutes. The tub drains in 13 minutes 20 seconds. If the stopper is out and the taps run full force, how long will it take the tub to fill? (And how much water will be wasted?)

Answer:

The tub will fill in 5 minutes........The cold faucet fills the tub in 400 seconds (1/400 per second), the hot faucet in 480 seconds (1/480 per second). The tub empties 1/800 of its contents per second. So with both faucets and the drain working together, 1/400 + 1/480 - 1/800, or 1/300 of the tub, gets filled each second. Therefore, the tub will be filled in 300 seconds, or five minutes. Since 1/800 of a full tub empties each second, the amount of water wasted  is 1/800 of a second X 300 seconds = 3/8 of a full tub.