Reggie was hiking on a 6-mile loop trail at a rate of 2 miles per hour

I think the term "loop" trail answers the confusion. Since, it's a loop so Cassie can go in the same direction as that of Regan or in the opposite direction and we need to find out which one takes lesser time. Per the calculations, heading in opposite direction takes lesser time (0.8 hours). Hence, it's the answer.

let t=cassie's time
3t+2(t+1)=6 miles
t=4/5=.8 hours

They are walking in opposite directions around a loop. He walks alone for one hour at a rate of 2 miles per hour, which means he walks two miles. Now, she begins walking from the same starting point moving the other direction around the loop, and they are 6-2= 4 miles apart. When objects move toward each other, we add their rates. Thus, they are closing the 4 mile gap at a rate of 5 miles an hour.

Rate x Time = Work

5 x Time = 4
Time = 4/5 or .8

Since the trail is a loop, the quickest way for Cassie to meet Reggie is to hike in the opposite direction of Reggie’s path:

We can let Reggie’s time = t + 1 and Cassie’s time = t, thus:

2(t + 1) + 3t = 6

2t + 2 + 3t = 6

5t = 4

t = 4/5 = 0.8 hours

Answer: A

Guess it just comes down to correctly knowing what a “loop system” trail actually is.

A loop trail is a circular like loop in which you end the hike at the same place you started.

For the purpose of this question, you can assume it’s a circular track.

Reggie travels for a +1 hour head-start. At 2 mph, he reaches mile marker 2 going clockwise around the 6 mile loop trail.

Cassie now has 2 options.

Case 1: She can come from behind clockwise in the Same Direction and Catch Up to Reggie. She will have to CLOSE a Gap Distance of 2 miles that Reggie created with the +1 hour head start.

Case 2: Or, she can come from the Opposite Direction that Reggie traveled and close a Gap Distance of 4 miles (from the starting Point to mile marker 2 where Reggie is at.


Case 1: since they will be traveling in the Same Direction, we need to SUBTRACT the individual Speeds to find their Relative Speed because Reggie is hindering the efforts of Cassie to close the 2 mile GAP.

Time to meet = Gap Distance / Relative Speed = 2 miles / (3 - 2) mph = 2 hours


Case 2: we should ADD their Individual Speeds to find the Relative Speed because Reggie is helping Cassie close the Gap Distance of 4 miles by moving in the Opposite Direction towards her.


Time to meet = Gap Distance / Relative Speed = 4 miles / ( 3 +
2) mph = 4/5 = .8 hour


Answer -A- .8 hour is the minimum Time

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