SOLUTION: 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)=150t^2 wh

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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)=150t^2 wh      Log On


   

Question 258295: 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)=150t^2 where t is in minutes.
a) How much water flows out of the tank in the first 3 minutes?
b)How many minutes does it take for the tank to empty completely?

I am completely lost any help would be great!!!!
Found 2 solutions by Alan3354, richwmiller:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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)=150t^2 where t is in minutes.
a) How much water flows out of the tank in the first 3 minutes?
b)How many minutes does it take for the tank to empty completely?
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What class are you in?
Can you use derivatives and integrals? Are you familiar with those?

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a)
f(3)=150*3^2
f(3)=150*3*3=450*3=1350
f(3)=1350
b)
6000=150*t^2
40=t^2
2sqrt(10)=t
t=6.32456 minutes