Tap A alone fills a tank in 24 hours. Tap A and tap B together fill the same tank in 15 hours. Tap B alone can fill the tank in how many hours?
Question
Tap A alone fills a tank in 24 hours. Tap A and tap B together fill the same tank in 15 hours. Tap B alone can fill the tank in how many hours?
Solution
Step 1: Determine the rate at which Tap A fills the tank. Since Tap A can fill the tank in 24 hours, its rate is 1/24 of the tank per hour.
Step 2: Determine the combined rate of Tap A and Tap B. Since they can fill the tank together in 15 hours, their combined rate is 1/15 of the tank per hour.
Step 3: Subtract the rate of Tap A from the combined rate of Tap A and Tap B to find the rate of Tap B. This is 1/15 - 1/24 = 9/360 = 1/40 of the tank per hour.
Step 4: Since the rate of Tap B is 1/40 of the tank per hour, it would take Tap B 40 hours to fill the tank on its own.
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