You sign up for a team mud run with a friend, only to find it’s a strangerelay race. From the starting point of the course is a massive mud field,stretching to the south. At the southern edge of the field is a paved roadwhich runs to the east. The rules of the race are as follows: the first teammatemust make it to the road, tag their partner, who then runs along the roaduntil the finish line. You’re in the last group of runners scheduled, so you watch a few of the earlier groups to study the race. You watch a team from the first group, where the first runner runs completelysouth, covering a distance of 2 miles, and tags their partner, who then hasto run 5 miles east to reach the finish line.In the next group is a pair that has a member that twisted their ankle afterarriving, and so the teammate had arranged to meet the partner at the finishline, and trudges through the mud field at an angle, so that when they reachthe road, the partner doesn’t have to run at all (but is quite exhausted uponreaching it, having gone well beyond 2 miles in the mud).You decide on a strategy to meet your partner partially along the road in thehopes of finding the fastest possible route through the course. Assuming youcan average 6 miles per hour through the mud, and your friend can average12 miles per hour on the road, how far along the road should you arrange tomeet?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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You sign up for a team mud run with a friend, only to find it’s a strangerelay race. From the starting point of the course is a massive mud field,stretching to the south. At the southern edge of the field is a paved roadwhich runs to the east. The rules of the race are as follows: the first teammatemust make it to the road, tag their partner, who then runs along the roaduntil the finish line. You’re in the last group of runners scheduled, so you watch a few of the earlier groups to study the race.

You watch a team from the first group, where the first runner runs completelysouth, covering a distance of 2 miles, and tags their partner, who then hasto run 5 miles east to reach the finish line.In the next group is a pair that has a member that twisted their ankle afterarriving, and so the teammate had arranged to meet the partner at the finishline, and trudges through the mud field at an angle, so that when they reachthe road, the partner doesn’t have to run at all (but is quite exhausted uponreaching it, having gone well beyond 2 miles in the mud).You decide on a strategy to meet your partner partially along the road in thehopes of finding the fastest possible route through the course. Assuming youcan average 6 miles per hour through the mud, and your friend can average12 miles per hour on the road, how far along the road should you arrange tomeet?

Expert Solution

Step 1

Let S be the starting point and F be the finishing point. Let O denotes the point where the massive mud ends from S.

The path SO is along the mud and OF is the paved road.

According to the question, given that:

SO = 2 miles, OF = 5 miles

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