swerve wrote: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

Let Reggie travel CLOCKWISE.
Since Reggie's rate = 2 mph, the distance traveled by Reggie in 1 hour = rt = 2*1 = 2 miles.

At this point, Cassie can travel clockwise to catch-up to Reggie or counterclockwise to meet him.
Test the time required if Cassie travels COUNTERCLOCKWISE, with the result that she and Reggie travel TOWARD EACH OTHER.
The reason:
If Cassie and Reggie travel toward each other, they WORK TOGETHER to cover the distance between them.
As a result, the time required for them to meet is likely to be minimized.

When people work together, ADD THEIR RATES.
Combined rate for Reggie and Cassie = 2+3 = 5 mph.
Of the 6-mile loop, 2 miles are traveled clockwise by Reggie in the first hour, leaving 4 miles between Cassie and Reggie when Cassie begins to travel counterclockwise.
Since their combined rate = 5 mph, the time for Cassie and Reggie to cover these 4 miles = d/r = 4/5 = 0.8 hour.
Since no answer choice is smaller than 0.8, we do not need to test the time required for Cassie to catch-up to Reggie if she travels clockwise.

The correct answer is A.