Question

A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.

Answer 1

Answer: 13.827 days (approximate)

A more accurate value would be 13.8271643518519

Round it however you need to.

======================================================

Step-by-step explanation:

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Let's see how many seconds there are in a day.

`1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=(24*60*60)/(1*1*1)\text{ sec}\\\\=86,400\text{ sec}\\`

I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".

There are exactly 86,400 seconds in 1 day.

This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.

----------

1 drop = 0.003 cubic inches approximately

x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.

0.003x = 3584

x = 3584/0.003

x = 1,194,666.66666667 approximately

Round up to the nearest whole number to get 1,194,667

The sink starts to overflow when we have 1,194,667 drops of water in it.

Divide this over 86,400 mentioned earlier.

(1,194,667)/(86,400) = 13.8271643518519 approximately.

Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827