Question

Hurry! A FedEx freight truck carries three tons of packages 660 miles on 90 gallons of diesel fuel from Miami, Fl to Atlanta, Ga. FedEx makes a graph to represent the miles per gallon the truck uses.

(a) Sketch a graph to represent the situation. Use one axis to represent the number of miles and the other axis to represent the number of gallons. Label your intercepts.
(b) What is the domain in this situation? explain you answer.
(c) What does the origin of the graph represent in this situation? explain your answer

Answer 1

(a) Truck carries 90 gallons of diesel fuel to 660 miles.

So, 1 gallon of diesel fuel to 660/90 = 22/3 miles.

30 gallons of diesel fuel to
`30()(22)/(3)` = 220 miles.

Hence, if x-axis represents the number of miles and y-axis represents the number of gallons, then, (660, 90) and (220, 30) are points on the graph.

Join (660, 90) and (220, 30), we get the graph of a line.

Note that (0, 0) is also a point on the line.

Equation of the line is
`y=(22)/(3) x`.

(b) x represents the number of miles. Therefore, the possible values for x is the closed interval [0, 660].

Hence, the domain of the function is [0, 660].

(c) Origin represents that the truck is not moving and there is no diesel fuel loaded in the truck.