SOLUTION: One runner passes another runner traveling in the same direction on a hiking trail. The faster runner is jogging 2 miles per hour faster than the slower runner. Determine how long

Question 908937: One runner passes another runner traveling in the same direction on a hiking trail. The faster runner is jogging 2 miles per hour faster than the slower runner. Determine how long it will be before the faster runner is 0.75 miles ahead of the slower runner.
What I have is r+2 would be part of the equation but I haven't figured out how to set up the problem correctly.
Found 2 solutions by mananth, jim_thompson5910:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
slow runner rate =x
faster runner rate = x+2
difference in rate = x+2-x=2 mph
d= 0.75
t=d/r
t=0.75/2
t= 0.375 hours
=22.5 minutes

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let runner A be the faster runner

Runner A: speed of r+2

Runner B: speed of r

Let's say we start the clock/stopwatch at the moment runner A passes runner B. Put another way, we can think of it as they are both starting at the same time at a starting line in a race. At the starting point, t = 0

Both runners are running for the same length of time (t) according to the time modeling described above. Let t be time in hours.

Distance runner A has ran: D = (r+2)*t = r*t + 2*t

Distance runner B has ran: D = r*t = r*t

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Subtract those distances: (Runner A) - (Runner B) = (rt + 2t) - (rt) = 2t

This difference is 2t

We want to know when the difference is 0.75 miles, so

2t = 0.75

t = 0.75/2

t = 0.375

It will take 0.375 hours

0.375 hours = 0.375*60 = 22.5 minutes

22.5 minutes = 22 minutes, 30 seconds

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There are multiple ways to answer, but I'd go with 22 minutes, 30 seconds

So it takes 22 minutes, 30 seconds for runner A to be 0.75 miles ahead of runner B.
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