Joe Fleet Can Jog At The Rate Of 8 Mph. Ron Pack Can Hike Carrying Camping Equipment At The Rate Of 4 Mph. They Leave From Opposite Ends Of A 44-mile Trail At The Same Time. How Far Does Each Travel If Ron Has 15 Minutes To Set Up Camp Before Joe Arr?


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Asuka Jr. answered
Joe Fleet has jogged a total of 30 miles (assuming he has maintained a punishing constant marathon rate at 8mph), and Ron Pack has hiked 14 miles.

This can be calculated by recognizing that Joe Fleet jogs at a speed of 2 miles per 15 minutes (8/4=2), and this means that when Ron has stopped to set up camp, Joe is still 2 miles away (the 15 minutes Ron has before Joe arrives).
So the distance traveled between them at the time Ron stopped is 42 miles (the full 44 miles of the length of the trail, minus the 2 miles distance that Joe remains at the time Ron begins setting up camp), and since Ron hikes at half the speed Joe jogs (again assuming a constant speed), their rate of travel between the two is 12 miles an hour (8+4), thus in 3 hours they travel 36 miles, subtracted from the 42 miles they BOTH spend travelling, leaves 6 miles, exactly the distance they collectively travel in 30 min (12/2). Thus they both travel for 3 1/2 hrs before Ron stopped to set up camp.
At 3.5 hrs, Ron has hiked a total of 14 miles, and Joe has traveled twice that distance, so 28 miles, but since Ron stops to set up camp, and Joe has to cover the remaining 2 miles in the 15 minutes Ron uses to set up camp, Joe has traveled a total of 30 miles (3.5x8+2=30).
Combined together, the total traveled distance then matches the 44 miles of the stated length of the trail (14+30=44), so the final answer, as stated above, is that:
Joe has jogged 30 miles.
Ron has hiked 14 miles.

Hope that helps, and you have a great day!
Asuka Jr.

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