Question

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

Ans(a):

Given that a FedEx freight truck carries three tons of packages 660 miles on 90 gallons of diesel fuel from Miami, FL to Atlanta, GA.

so that means speed of the truck is

speed = distance/time = 660/90 miles per gallon

hence slope of the equation will be

m=660/90 = 66/9= 22/3

There is no information about initial cost or any initial value so that means y-intercept b=0

plug value of m and b into y=mx+b

so we get equation y=22/3x+0

Where x is the number of gallons and y is the number of miles

Now we can easily graph this equation to get the required graph.

when x=0 then y=22/3x=22/3*0=0

so first point is (0,0)

when x=3 then y=22/3x=22/3*3=22

so second point is (3,22)

Now we join them by a line to get the graph

Ans(b):

clearly number of gallons can't be negative. It is also given that truck uses 90 gallons of diesel fuel. so the domain can be any real number from 0 to 90 or we can write domain as [0,90].

Ans(c):

Origin of the graph represents that if there is no gallons of fuel used then there will be no distance traveled.