Question

Zen the

20,1.
A water tank is being filled by pumps at a constant rate. The volume of water in the tank V, in gallons, is
given by the equation:
v(t) = 65t + 280, where t is the time, in minutes, the pump has been on
(a) At what rate, in gallons per minute, is the (b) How many gallons of water were in the tank
water being pumped into the tank?
when the pumps were turned on?
Ult=65 1280
v101=6510) +250=280
rate is 65
wakers of gallon
tank had 280 gallons.
(c) What is the volume in the tank after two hours (d) The pumps will turn off when the volume in
of the pumps running?
the tank hits 10,000 gallons. To the nearest
minute, after how long does this happen?
edict

Answer 1

(a) 65 gallons per minute

(b) 280 gallons

(c) 8080 gallons

(d) 150 minutes.

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)