Two cars start at the same time and travel at different constant rates. Which car is traveling faster?

Question

Two cars start at the same time and travel at different constant rates. A graph for Car A passes through the point (0.5, 27.5), and a graph for Car B passes through (4, 240). Both graphs show distance in miles and time in hours. Which car is traveling faster? Explain.

Answer 1

Assuming the coordinate graph is plotting distance = y(miles) versus time = x(hours)

Also need to assume that both cars start at the origin and travel to the points given

Then car A's speed is given by the slope = Δy/Δx = 27.5/0.5 = 55 mph

car B's speed is slope = 240/4 = 60 mph

So car B has greater slope on this graph indicating greater speed and is thus travelling faster.