Answer: it will take 1 hour before the second runner reaches the first runner
Step-by-step explanation:
Let t represent the time it the first runner to cover a certain distance.
Speed of the first runner is 6 miles per hour.
Distance = speed × time
Time = distance / speed
Distance covered by the first runner
in t hours at 6 miles per hour is 6t
Fifteen minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. This means that for the to meet, the second runner will cover the same distance covered by the first runner at a time of t - 15 minutes = (t - 1/4) hours. Therefore
Distance covered at 8 miles per hour at (t - 1/4) hours
would be 8(t - 1/4) = 8t - 2
Since they would cover the same distance, then
6t = 8t - 2
8t - 6t = 2
2t = 2
t = 2/2 = 1
