Question

Two cars are traveling to the same campground along the same route. The cars began at the same place but at different times. Car A began the trip at noon, and car C began the trip at different time before noon. The miles traveled by Cars A and C are represented respectively, by the following graph and equation. image image At what time, if ever, will car A pass car C? Describe any assumptions you made and justify your answer. Enter your answer, your description, and your justification in the space provided.

Answer 1

Explanation:

the equation for car C shows us that it had already a head start of 20 miles at t = 0 (when car A started).

the slope 68 tells us that it then travels with the speed of 68 mph.

for car A we need to find its slope (= speed) too to get the equation for it.

the only points on the line in the graph with integer coordinates I found at 5 hours and 350 miles, and at 0 hours and 0 miles.

so, the slope (y diff./x diff.) is

350/5 = 70.

that means car A travels with the speed of 70 mph.

the y-intercept is 0 (as it is the origin).

the equation for car A is therefore

D = 70t

car A will overtake car D, when both distances from the starting point are equal :

70t = 68t + 20

2t = 20

t = 10 hours

car A will overtake car C after 10 hours.