#### A Math Forum Project

 ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Student Version

### Search and Rescue: Part II - posted January 29, 2001

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# Search and Rescue: Part II

### Introduction

Now that you are a licensed Search and Rescue helicopter pilot, you are ready to help engineers decide where to build the new rescue base. Two campgrounds are placed near the lakes on opposite sides of the mountains. Use the applet to experiment.

1. How many places could you put the new rescue base in order to guarantee equal response time to either campground?

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.

3. The engineers have come back and reported that there will likely be twice as many campers in the Moose campground as in the Trout campground. This means that, on average, twice as many rescue missions will be required for the Moose campground. Based on this new information, where would you now position the rescue base?

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

### Highlighted solutions:

 From: Will S., age 15 School: McLean High School, McLean, VA

```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.
```

 From: Eric R., age 16 School: McLean High School, McLean, VA

```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 103.8-310 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
```

### 3 students received credit this week.

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