A cubic mile tank full of water, you put a hole that empties at 100 gallons a second. Emptying takes how long

Question

A cubic foot of water holds 7.48052 gallons of water

Answer 1

1 cubic mile = 5280 X 5280 X 5280 = 147197952000 cubic feet.

If each cubic foot holds 7.48052 gallons of water, then the total gallons in the tank are:

147197952000 X 7.48052 = 1101117223895.04 gallons

If you drain 100 gallons a second, the total time to empty would be:

1101117223895.04 / 100 = 11011172238.9504 seconds

About 18,206.3 weeks.

Answer 2

There are 7.48 gal per cubic foot as you have noted. There are 5280 feet per mile or 5.28 x 10^3 ft/mi. Now cube this and we have 5.28^3 x 10^9 or 147.198 x 10^ 9ft^3. Finally multiply that by 7.48 gal/ft^3 to get 1101.04 x 10^9 gallons or 1.101 x 10^12 gallons. Emptying at a rate of 100 gal/sec we get:

(1.101 x10^12)/100 seconds or 1.101 x 10^10 seconds

since there are 86400 seconds per day it would take

(1.101/8.64 ) x 10^6 days or 127.4 x 10^3 days to empty the tank.

With 365 days per year this result in 349 years.

Answer 3

One mile is 1760 yards, there are 3ft in a yard, so therefore there are 1760*3= 5280ft in one mile. We can cube this to get the number of cubic feet in one cubic mile= (5280^3)= 1.47197952 x 10^11 cubic feet.

100 gallons is equivalent to 100/7.48052= 13.36805463 cubic feet per second.


The amount that 1.47197952 x 10^11 can hold is 1.47197952 x 10^11/13.36805463 =1.01117224 x 10^10 seconds, dividing by 3600 to convert to hours gives 3058658.956 hours, dividing by 24 to convert to days, 127444.123 days, dividing by 365.24 to convert to years gives 348.932 Years. You will be dead before it empties.

Answer 4

1 mile³ = 5280^3 ft³
= 147.2 * 10^9 ft³

= 147.2 * 10^9 * 7.48052 = 1.101 *10^12 gallon
when the hole empties 100 gallons/s
so the time to empty the tank
= 1.101 *10^12 /100
= 1.101 * 10^10 seconds
= 3.059 *10^6 hours
= 348.97 years