
ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary 
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Search and Rescue: Part II
Introduction
Teacher Support Page For question 1, we didn't ask you to explain how you got your answer, but we really wanted to know! A lot of you didn't explain. Perhaps our fault, but all the Problems of the Week ask you to explain your answers. That's one of the points of these puzzles  to explain your thinking so clearly that someone who doesn't understand the answer can learn something.
In question 2, some of you didn't include the distances from the camps to the new base. I'm not sure why, as that would make it clearer for the engineers. Even if the answer can be figured out using only the headings, it's a good idea to give redundant information. Did you ever hear the expression, "Measure twice, cut once"? That's to make sure no mistakes have been made.
Some of the answers to question 3 were interesting: "In the same place. Even if there are more of them, why should the campers at Moose have access to faster medical service then those at Trout?" However, we were looking for a camp that was twice as close to the more populated camp. Some of you put the camp a little closer  some even put it in the place we wanted  but many of you didn't justify the new distance very well.
We have a couple of clear explanations for answers to this puzzle below. Take a look.
 Jody

1. How many places could you put the new rescue base in order to guarantee equal response time to either campground? an infinite number of places, you can postition the base anywhere as long as there is an equal distance to each camp. 2. Explain to the engineers where they should build the rescue base and why, using precise information from your map. Remember that the engineers need very precise instructions. The Base should be at a heading of 135 degress from the Moose camp and 287.6 from the trout camp. This way it is exactly 2.7 Miles from each camp, allowing equal rescue time. 3. The engineers have come back and reported that there will likely be twice as many campers in the Moose campground. This means that there will be on average twice as many rescue missions required to the Moose campground. Based on this new information, where would you now position the rescue base? Beacuse it needs to twice as close to the Moose Camp you'd put the new base at a heading of 147 degress from the Moose camp so it is 1.8 miles away from it. And 288.1 degress from the Trout camp so it's 3.6 miles away. This way the number of rescues will be equally expressed with the number of people.

1. How many places could you put the new rescue base in order to guarantee equal response time to either campground? An infinite number of places but only two with minimized travel distance. 2. Explain to the engineers where they should build the rescue base and why, using precise information from your map. Remember that the engineers need very precise instructions. 2 places minimize the distance. A) North of the mountains 132.4 to moose, and 290.2 to trout. This means that it is 2.7 miles to each camp. B)South of the mountain 112.3 to moose, and 310.3 to trout. this means 2.6 miles to each park. This position is the closest base that is equal distance between the two camps. The distance could have been shorter if the helocopters would have been alowed to fly over the mountains. 3. The engineers have come back and reported that there will likely be twice as many campers in the Moose campground. This means that there will be on average twice as many rescue missions required to the Moose campground. Based on this new information, where would you now position the rescue base? In this problem I thought that "average twice as many rescue missions required to the Moose campground" was very important. I took this to mean that, I should form a ratio using the distances between the two camps. The ratio would have to consist of a number that was half of the other number. This base would also still have to be as close to the two camps as possible. I chose 103.8310 as my position in this problem. This position puts the base 3.6 miles to trout, and 1.8 miles to moose. I have changed my mind however and decided to keep the camps in the same place. Having the distance to trout longer was not acceptable. Responce time to either camp needs to be minimized. In this position all emergency call responce times will be the smae
Katharine C., age 13  Issaquah Middle School, Issaquah, WA
Eric R., age 16  McLean High School, McLean, VA
Will S., age 15  McLean High School, McLean, VA