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

Question

Reggie was hiking on a 6-mile loop trail at a rate of 2 miles per hour. One hour into Reggie’s hike, Cassie started hiking from the same starting point on the loop trail at 3 miles per hour. What is the shortest time that Cassie could hike on the trail in order to meet up with Reggie?

(A) 0.8 hours
(B) 1.2 hours
(C) 2 hours
(D) 3 hours
(E) 5 hours

(A) 0.8 hours
(B) 1.2 hours
(C) 2 hours
(D) 3 hours
(E) 5 hours

So this question is from the MGMAT ROADMAP. I understand the first part of solution provided in it, that it will take cassie 2 hours to catch up to Regan. However, the solution also calculates time if cassie would do the hike in the opposite direction. Now this is really confusing to me. There is no methodology that I take from it that how Cassie is able to hike miles 6 miles in reverse while reggie is only able to hike 2 miles for that direction.

Answer is A.

Please help.

Answer is A.

Please help.

ScottTargetTestPrep · Accepted Answer

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

DAllison2016 · Answer

Didn't get this (assumed they were both hiking in the same direction).

ext{speed} = \frac{	ext{distance}}{	ext{time}}

ext{distance travelled in 1 hour: }2 	ext{ miles } (	ext{speed} 	imes 	ext{time}) .

ext{Distance from }\color{red}{	ext{end of the trail (anticlockwise)}}: 6 - 2 = 4 	ext{ miles} .

Speed that they are coming together:  3mph + 2mph = 5mph .

ext{Time} = \frac{	ext{distance}}{	ext{speed}} = \frac{4}{5} = 0.8

hsbinfy · Answer

we don't need to assume here the direction.we need to find which will take less time

so there are 2 cases

1)both moving in same direction...then time would be 2 hrs

2)both moving in opp direction then time would be 0.8 hrs

as we need the shortest time it would be the second case

sudhirgupta93 · Answer

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.

gracie · Answer

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

dannythor6911 · Answer

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

Rate x Time = Work

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

Fdambro294 · Answer

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

Posted from my mobile device

Wadree · Answer

Reggie went in 1 hour = 2 
So....reggie got 4 more to go.....
Now....cassie started.....but instead of going da same way reggie went....she go da other way around..... 
So now.... There is 4 distance between cassie and Reggie...... Both start going towards each other......
Cassie speed = 3 ...... Reggie speed = 2 .... 
Cassie go in 1 hour = 3 ...... And Reggie go in 1 hour = 2 
In 1 hour....da distance between them decrease by 2 + 3 = 5 
So 4 distance decrease in = 4 / 5 = 0.8 hour .....

!nah id win!

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

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

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