Final answer:
The walker's speed is 16.67 miles per hour, and the cyclist's speed is 25 miles per hour. This is determined using the relationship between speed, distance, and time, alongside the information that the cyclist travels 1.5 times faster than the walker and the distance between them after 1.5 hours is 12.5 miles.
Step-by-step explanation:
To calculate the speeds of the cyclist and the walker, we will use the relationship between speed, distance, and time. Since the speeds of the cyclist and the walker are related by a factor of 1.5, if we call the walker's speed w (in miles per hour), then the cyclist's speed is 1.5w. They have traveled for 1.5 hours and the distance between them is 12.5 miles at that time.
Considering the distance traveled by each in 1.5 hours:
-
- Distance by walker = w * 1.5 hours
-
- Distance by cyclist = 1.5w * 1.5 hours
The difference in distances is given as 12.5 miles:
(1.5w * 1.5) - (w * 1.5) = 12.5
Simplifying gives us:
2.25w - 1.5w = 12.5
0.75w = 12.5
w = 12.5 / 0.75
w = 16.67 miles per hour (walker's speed)
Now, we calculate the cyclist's speed:
Cyclist's speed = 1.5 * 16.67
Cyclist's speed = 25 miles per hour