Question

A runner starts at the beginning of a runners' path and runs at a constant rate of 6 mi/hr. Fifteen minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. How long will it take the second runner to reach the first?

Answer 1

45 minutes

Explanation:

let after t hours they meet after the second runner starts.

15 minutes=1/4 hour.

6(t+1/4)=8t

6t+6/4=8t

8t-6t=6/4

2t=3/2

t=3/2* 1/2=3/4 hours=45 minutes

Answer 2

Answer: it will take 1 hour before the second runner reaches the first runner

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