Answer:
(a) 65 gallons per minute
(b) 280 gallons
(c) 8080 gallons
(d) 150 minutes.
Step-by-step explanation:
Water is filled up by pumps into a tank at a constant rate.
The volume of water in the tank V, in gallons, is given by the equation
V(t) = 65t + 280 ......... (1), where t is the time, in minutes.
(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)
(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)
(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)
(d) The tank has a capacity of 10000 gallons of water.
So, if the tank starts to overflow after t minutes, then
10000 = 65t + 280
⇒ 65t = 9720
⇒ t = 149.53 minutes ≈ 150 minutes (Answer)
