Short Answer 
The process to understand the runners’ speeds involves three steps: defining the slower runner’s speed as x and the faster runner’s speed as x + 2, setting up an equation based on the time taken to meet (1.1 hours), and solving this equation to find the slower runner’s speed as approximately 2.44 mph and the distance they meet at as about 4.884 miles from the starting point.
Step 1: Understanding the Speeds
Let the speed of the slower runner be denoted as x miles per hour. The faster runner’s speed will then be (x + 2) miles per hour since they run 2 miles per hour faster. This sets the stage for calculating their respective distances covered over a specific time period.
Step 2: Setting Up the Equation
The time duration taken for the runners to meet is 1 hour and 6 minutes, which equals 1.1 hours. In this time, the distance the slower runner covers is x, while the faster runner covers (x + 2) * 1.1. The relationship between their distances can be expressed as:
- 2x = (x + 2) * (1.1)
This equation is crucial to determine the value of x.
Step 3: Solving the Equation and Finding Distances
Now, simplify the equation to isolate x:
- 2x = 1.1x + 2.2
- 0.9x = 2.2
- x ‚Äöaa 2.44 miles per hour (slower runner)
- Speed of faster runner ‚Äöaa 4.44 mph
Finally, plug x back into the original equation to find the meeting distance: the runners meet approximately 4.884 miles from the starting point.