Problem 8 – Putting Out the Campfire
The following is a famous calculus problem first posed and solved by Pierre de Fermat in the 1700s.
Suppose that you are camping near a river (you are 10 feet away) and you see a campfire that’s getting out of hand in the distance (the campfire is 30 feet away from the river and the stretch of river between you and campfire’s location is 50 feet) . You have a bucket, but your bucket is empty. You know that you should run to the river with the bucket, get the water, and then run to the fire and put it out. Suppose that when you carry an empty bucket your running speed is 1.5 times of the running speed when the bucket is filled with water. What’s the optimal path? Where along the river should you go to get the water so that you will reach the campfire as quickly as possible?
Please send all solutions to mathpotw@acu.edu by 5:00 PM on Thursday, December 2nd. This will be our last problem of the semester.
