10. A bathtub with two taps can be filled in 15 minutes using only the cold wate

Question

10. A bathtub with two taps can be filled in 15 minutes using only the cold water tap. It can be filled in 10 minutes using only the hot water tap. The flow of each tap is not changed when both taps are turned on. It takes 20 minutes to drain the full tub. Starting with an empty tub and the drain plug in place, the cold water is turned on. Three minutes later the hot water is also turned on, and three minutes after that the drain plug is removed. How many additional seconds after the plug is removed would it take to fill the tub?

Explanation / Answer

Time taken by cold water tap to fill the bathtub = 15 min

Time taken by hot water tap to fill the bathtub = 10 min

Time taken to drain = 20 minutes

So in 1 minute, 1/15th of tub will be filled by cold water, 1/10th tub will be filled by hot water and 120th tub will be drain (if left open)

For first three minutes:

Cold water and drain are working

Tub Filled = 3 * (1/15 (water incoming) - 1/20 (water outgoing)) = 1/20

For the next three minutes

Cold water, hot water and drain are working

Tub Filled = 3 * (1/15 (water incoming from cold tub) + 1/10 (water incoming from hot tub) - 1/20 (water outgoing)) = 7/20

After 6 minutes, the drain plug is removed, so only hot and cold water are working

Tub Filled in first 6 minutes = 1/20 + 7/20 = 8/20

Tub left to fill = 12/20

Incoming flow per minute = (1/15 + 1/10)

(1/15 + 1/10) * x = 12/20

1/6 * x = 12/20

x = 72/20 = 3.6 minutes

TIme in seconds = 3.6 * 60 = 216 seconds

Hence amount of additional seconds required to fill the tub completely = 216 seconds

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