Question

A cyclist's speed is 1.5 times faster than a walker's speed. They simultaneously start moving in the same direction from the same point and, after 1.5 hours, the distance between them is 12.5 miles. What are their speeds?

Answer 1

The walker's speed is approximately 16.67 miles per hour, and the cyclist's speed is approximately 24.99 miles per hour.

Step-by-step explanation:

To solve this problem, let's assume the walker's speed is x miles per hour. Since the cyclist's speed is 1.5 times faster, the cyclist's speed would be 1.5x miles per hour. After 1.5 hours, the distance between them is 12.5 miles.

1. Distance covered by the walker in 1.5 hours = x * 1.5 = 1.5x miles
2. Distance covered by the cyclist in 1.5 hours = 1.5x * 1.5 = 2.25x miles
3. The distance between them is the difference between the distances covered by the cyclist and the walker: 2.25x - 1.5x = 0.75x miles

Given that 0.75x miles = 12.5 miles, we can solve for x: x = 12.5 / 0.75 = 16.67 miles per hour.

Therefore, the walker's speed is approximately 16.67 miles per hour and the cyclist's speed is approximately 1.5 times faster, or 24.99 miles per hour.