Question

·A long distance runner started on a course running at an average speed of 6

mph. One hour later, a second runner began the same course at an average
speed of 8 mph. How long after the second runner started will the second
runner overtake the first runner? I also need the work pls help!

Answer 1

The second runner will overtake the first runner 3 hours after the second runner starts, as the second runner runs at a speed 2 mph faster than the first runner.

Step-by-step explanation:

The problem involves calculating the time it will take for the second runner to overtake the first runner. This is a classic relative motion question where we need to determine when the two runners will be at the same position. Since the first runner starts 1 hour earlier and runs at 6 mph, by the time the second runner starts, the first runner is already 6 miles ahead. The second runner runs at 8 mph, which is 2 mph faster than the first runner.

To find out how long it will take for the second runner to catch up, we can set up the following equation where t is the time in hours after the second runner starts:

Distance covered by first runner = Distance covered by second runner

6t + 6 = 8t

By solving this equation, we get:

6 = 8t - 6t

6 = 2t

t = 3 hours

So, the second runner will overtake the first runner 3 hours after the second runner starts.