A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gallons per hour is given by the function f (t) = 300 t^2 where t is in minutes.

How much water flows out the tank in the first 7 minutes?

How many minutes does it take for the tank to be completely empty?,

The volume of the gallon is 6000 gallon

the rate of water flow per min is f (t) = 300t^2

a] amount of water that flowed in the first 7 minutes=7/60 hours will be:

f (7) = 300 (7/60) ^2

solving the above we get

f (7) = 7/12 gallons

b] The time taken for the tank to be empty will be as follows:

amount of water that will flow out for the tank to be empty will be 6000 gallons

thus,

6000=300t^2

this can be simplified to

20=t^2

t^2-20=0

solving this we get:

t=-2√5 or 2√5

the time taken for the tank to be empty will be t=2√5 hours=5.4721 hours