Homework SourseA valve in a full 6000 gallon water tank is slowly opening W
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.
a) How much water flows out of the tank during the first 2 minutes?
b) How long does it take for the tank to empty?
Please show steps!
a) How much water flows out of the tank during the first 2 minutes?
b) How long does it take for the tank to empty?
Please show steps!
Solution
the flow rate given is in gallon per hour. so to convert to gallon per minute, f(t) = 300*t^2 /60 =5*t^2 A) water flow is integral of f(t)dt for time interval 0 to 2 so integral is 5t^3 / 3 , putting the limits, 40/3 gallon. b) for volume flow of 6000 gallon. 5t^3 /3= 6000 t = 15.326 min.
