My old house had a leaky sink. I used to shave in this sink by filling up the si

Question

My old house had a leaky sink. I used to shave in this sink by filling up the sink with water and then shaving while the water slowly leaked out. Sometimes the water would completely run out before I was finished. I made some calculations. It took 30 seconds to fill up the sink completely after I'd turned on the tap. It took 3 minutes for the completely-filled sink to leak out and be empty. It took me 2 minutes to shave. I figured that the sink had to be at least 5% full in order to have enough water for me to shave effectively. What is the minimum amount of time I should turn on the water to be sure I have enough water to finish shaving without having to add more? (Note: I turn off the water before I start to shave, and I start shaving immediately upon turning off the water.)

Explanation / Answer

for sink to be 100% empty time taken = 3 minutes

so in 2 minutes sink will be empty by 2/3*100= 66.67%

plus we need 5% minimum level after two minutes, so minimum water level in the sink to be maintained before the tap is turned out should be 66.67+5 = 71.67%

so time taken to fill 71.67% percent will be 30/100*71.67 = 21.5 seconds

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