Question

A pump is being used to fill a 1400-gallon tank. After the pump has run for 2 minutes the tank contains 110 gallons of oil. After 5 minutes the tank contains 200 gallons of oil. Assume the pump fills oil at a constant rate.

(a) Write a linear model that describes the gallons of oil (G) in the tank in terms of the time (t) since the pump was started.
(b) How much oil is in the tank after the pump has been running for 13 minutes?
(c) At what time, will there be 890 gallons of oil in the tank?
(d) What is the t-intercept for this equation? What does it represent in terms of the situation?

Answer 1

See below

Explanation:

From 2 minutes to 5 minutes the pump puts in (200-110) = 90 gallons ...in 3 minutes....so the rate of the pump is 30 gal / min

at two minutes the pump has put in 30 x 2 = 60 gallons......so there was 50 gallons in the tank to start ( 50 + 60 = 110)

the equation becomes :

G = 50 + 30 t

where t = minutes

and 50 is the initial volume in the tank

For 13 minutes G = 50 + 30 (13) = 440 gallons

For 890 gallons 890 = 50 + 30 t

840 = 30 t

t = 28 minutes

t intercept occurs when G = 0

0 = 50 + 30 t

t = - 5/3 minute <====this is the amount of time before measurements were taken.....or the time for the pump put in 50 gallons before the start