A runner starts at the beginning of a cross country course running at a constant rate of 6 miles per hour. Five minutes later a second runner begins at the same point,
second runner will lose.
To solve this problem, we can break it down into steps:
Step 1: Find the distance covered by the first runner.
Given that the first runner is running at a constant rate of 6 miles per hour, we can calculate the distance covered by using the formula: Distance = Rate × Time. Since the first runner starts running 5 minutes earlier, we can convert the 5 minutes into hours by dividing it by 60: 5 minutes ÷ 60 minutes per hour = 5/60 hours. Thus, the distance covered by the first runner is: Distance = 6 miles per hour × 5/60 hours.
Step 2: Find the distance covered by the second runner.
Since the second runner starts 5 minutes later than the first runner, that means the second runner has been running for 5 minutes less than the first runner. Therefore, the second runner has been running for 5/60 hours less than the first runner. To find the distance covered by the second runner, we can use the formula: Distance = Rate × Time. Thus, the distance covered by the second runner is: Distance = 6 miles per hour × (total time - 5/60 hours).
Step 3: Find the time it takes for the second runner to catch up to the first runner.
In order for the second runner to catch up to the first runner, their distances covered need to be equal. So we can set up the equation: Distance of first runner = Distance of second runner. Substituting the values from steps 1 and 2, we get: 6 miles per hour × 5/60 hours = 6 miles per hour × (total time - 5/60 hours). Now we can solve for the total time it takes for the second runner to catch up to the first runner.
By following these steps, you can find the answer to this problem.