Question

1. a cyclist travels north along a road at a constant speed of 15 miles per hour. at 1:00 p.m., a runner is 40 miles away, running south along the same road at a constant speed. they pass each other at 3:00 p.m. what is the speed of the runner?

Explanation:

Step1: Calculate time elapsed

Time between 1:00 PM and 3:00 PM is $3 - 1 = 2$ hours.

Step2: Calculate total distance covered

The initial distance between them is 40 miles, so together they cover 40 miles in 2 hours.

Step3: Find combined speed

Combined speed = $\frac{\text{Total Distance}}{\text{Time}} = \frac{40}{2} = 20$ miles per hour.

Step4: Solve for runner's speed

Let $v_r$ = runner's speed, cyclist's speed $v_c = 15$ mph. Combined speed: $v_r + v_c = 20$.
$v_r = 20 - 15 = 5$ miles per hour.

Answer:

5 miles per hour