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?,
Accepted Solution
A:
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=-2β5 or 2β5 the time taken for the tank to be empty will be t=2β5 hours=5.4721 hours