1.5 * 10^22 gallons, water filling at the rate of 2 gallons first minute, 4 gallons second minute, etc..
The total at each minute is Summation ( 2^i from i=1 to i=n )
From the Wikipedia page on summation we get:
For our problem a=2, m=1, n = the thing we don't know, and the total should be 1.5 * 10^22
1.5 * 10^22 = ( (2^1) - (2^n) ) / ( 1-2 )
1.5 * 10^22 = ( 2 - 2^n ) / (-1)
-1.5 * 10^22 = 2 - 2^n
2^n = 15,000,000,000,000,000,000,002
ln ( 2^n ) = ln ( 15,000,000,000,000,000,000,002 )
n * (ln 2) = ln ( 15,000,000,000,000,000,000,002 )
n = ln ( 15,000,000,000,000,000,000,002 ) / (ln 2)
n = 51.062337154 / 0.69314718056
n = 73.6673805883
But remember the formula:
The number of minutes the tank is being filled is the n-1 on top of the summation symbol, so the minutes we want is n-1, not n.
n - 1 = 72.6673805883
.6673805883 * 60 = 40.042835298
It would take 73 minutes (rounded up to the nearest minute) or 72 minutes 40 seconds (rounded up to the nearest second) to fill the tank.
Note:
15,000,000,000,000,000,000,000 gallons in the problem
9,200,000,000,000 gallons behind the hoover dam
326,000,000,000,000,000,000 gallons of water in the whole world
15,000,000,000,000,000,000,000 / 326,000,000,000,000,000,000 = about 46
The tank in the problem holds about 46 times as much water as there is in the whole world.