Question

The travel time between two cities is inversely proportional to the average speed. A train travels between the cities in 3 hours at an average speed of 65 mph. How long would it take to travel between the cities at an average speed of 80 mph? Round to the nearest tenth if necessary. LABEL!

Answer 1

t = 2.4 hours

Since travel time and average speed are inversely proportional, we can create a function where (time)(speed) = k, where k is some constant number. Since time is 3hrs and average speed is 65mph, and our new speed is 80mph, we can create a new equation since they are both equal to constant k.

Thus, since (65mph)(3h) = k and (80mph)(time) = k,

(65)(3) = (80)(t)

Then, using algebra, we solve for t and get

t = 2.4 hours