Starting at 9 A. M. you hike for 3 hours at an average speed of 5 mph. You stop for lunch from noon until 3 P. M. What is your average speed over the interval from 9 A. M to 3 P. M.?

The average speed over the interval from 9 A. M. to 3 P. M. is 2.5 mph.

Explanation:

We can calculate the average speed as:

s = (s₁ + s₂) / n = (5 mph + 0 mph) / 2 = 2.5 mph

where:

s=average speed over the entire interval (9 A. M. to 3 P. M.)

s₁: average speed during the hiking (interval from 9A. M. to 12 A. M.)

s₂: average speed during the lunch (interval from 12 P. M to 3 P. M.)

n: number of intervals