#### A Math Forum Project

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

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### Earthquake 4 - posted February 21, 2000

Try Earthquake 1, Earthquake 2, and Earthquake 3 before you do this problem.
On January 12, 2000, an earthquake occurred somewhere on this map. Three seismograph stations measured time differences between P and S waves.

1. What is the distance from each seismograph (S1, S2, S3) to the epicenter? (Hint: Use the graph.)

2. Enter these distances in the boxes labeled S1 Distance, S2 Distance, and S3 Distance. Notice that the radius of each circle adjusts. Where is the epicenter? How can you tell?

3. (Bonus) Last week, we determined that data from one seismograph can only determine the circle along the perimeter of which the epicenter must lie. This week, we found that data from three seismographs give an exact location. What could you learn from only two seismographs? How about four or more?

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Most students got the first two questions right.

For question 1, some answers were approximated, and that was okay. Sometimes, though, the order of the numbers was wrong, considering that they are all found on a line whose slope is greater than 0. It's true that it was difficult to read the precise numbers from the graph, but students should get the order of the numbers correct - that is, all three numbers should be greater than or equal to 12 and less than 15, AND go in this order: s2 -> s1 -> s3.

For question 2, most students got this right, but their explanations were not always good enough. Some students didn't talk about circles, and some talked about diameters and other things that didn't seem that relevant to the solution.

For the bonus question, about half of the submissions received credit. The common mistakes were to think that four seismographs would give you more information than three seismographs, and that two seismographs would give you an area of possible locations of the epicenter. We were especially impressed by the students who realized that any number more than three seismographs would give you the same information as three seismographs.

There didn't seem to be a transfer between what the graph showed and how the student would interact with the problem. When I (Suzanne) tried the problem myself, I ignored the graph and just started playing with the three values until they all intersected.

### Highlighted solutions:

 From: Ryan B., age 14Mac W., age 14 School: Issaquah Middle School, Issaquah, WA

```Page Week 4

1. What is the distance from each seismograph (S1, S2, S3) to the epicenter?
(Hint: Use the graph.)

Station one is 13 miles away from the epicenter, station 2 is about 12 miles
away from the epicenter, and station 3 is about 14 miles away from the
epicenter.

2. Enter these distances in the boxes labeled S1 Distance, S2 Distance, & S3
Distance. Notice that the radius of each circle adjusts. Where is the
epicenter?  How can you tell?

The epicenter is just a little bit above the Town Dump, we can tell because it
is where all three P&S waves meet.

3. (BONUS) Last week, we determined that data from one seismograph can only
determine the circle along which the epicenter must lie. This week, we found
that data from three seismographs gives an exact location. What could you
learn from only 2 seismographs? How about 4 or more?

------------------------------------
```

 From: Jeff B., age 13Ashok K., age 13 School: Issaquah Middle School, Issaquah, WA

```Page Week 4

1. What is the distance from each seismograph (S1, S2, S3) to the epicenter?
(Hint: Use the graph.)

S1: approx. 13 miles
S2: approx. 12 miles
S3: approx. 14 miles

2. Enter these distances in the boxes labeled S1 Distance, S2 Distance, & S3
Distance. Notice that the radius of each circle adjusts. Where is the
epicenter?  How can you tell?

It is slightly north of the town dump, because all the circles touch in that
point.

3. (BONUS) Last week, we determined that data from one seismograph can only
determine the circle along which the epicenter must lie. This week, we found
that data from three seismographs gives an exact location. What could you
learn from only 2 seismographs? How about 4 or more?

2 seismographs will give you two possible locations, and 4 or more
seismographs will still give only the one epicenter.

------------------------------------
```

 From: Jamin S., age 13Chris I., age 13 School: Issaquah Middle School, Issaquah, WA

```Page Week 4

1. What is the distance from each seismograph (S1, S2, S3) to the epicenter?
(Hint: Use the graph.)

The distance between S1 and the epicenter is 13 miles S2 is 12 miles and S3 is
14.5 miles away.

2. Enter these distances in the boxes labeled S1 Distance, S2 Distance, & S3
Distance. Notice that the radius of each circle adjusts. Where is the
epicenter?  How can you tell?

The epicenter is a little above the Town dump you can tell because that is
where the siesmograph circles intersect.

3. (BONUS) Last week, we determined that data from one seismograph can only
determine the circle along which the epicenter must lie. This week, we found
that data from three seismographs gives an exact location. What could you
learn from only 2 seismographs? How about 4 or more?

From 2 seismographs you would know where 2 possible locations of the epicenter
was and 4 you would know the exact location but you only need three.

------------------------------------
```

 From: Aaron D., age 12Paul J., age 15 School: Issaquah Middle School, Issaquah, WA

```Page Week 4

1. What is the distance from each seismograph (S1, S2, S3) to the epicenter?
(Hint: Use the graph.)
S1=13 miles
S2=12 miles
S3=14 miles
2. Enter these distances in the boxes labeled S1 Distance, S2 Distance, & S3
Distance. Notice that the radius of each circle adjusts. Where is the
epicenter?  How can you tell?
The Town Dump
Because the epicenter must be at a point on all of the cicles the epicenter
must be were they converge

3. (BONUS) Last week, we determined that data from one seismograph can only
determine the circle along which the epicenter must lie. This week, we found
that data from three seismographs gives an exact location. What could you
learn from only 2 seismographs? How about 4 or more?

From 2 you can eliminate it to two points

Whith 4 or more you get the same result as three

------------------------------------
```

### 50 students received credit this week.

Jared A., age - Issaquah Middle School, Issaquah, WA
Nelson A., age 12 - Issaquah Middle School, Issaquah, WA
Alex B., age 12 - Issaquah Middle School, Issaquah, WA
Amy B., age 13 - Issaquah Middle School, Issaquah, WA
Brooke B., age 14 - Issaquah Middle School, Issaquah, WA
Hana B., age - Issaquah Middle School, Issaquah, WA
Jeff B., age 13 - Issaquah Middle School, Issaquah, WA
Marissa B., age 13 - Issaquah Middle School, Issaquah, WA
Megan B., age 13 - Issaquah Middle School, Issaquah, WA
Ryan B., age 14 - Issaquah Middle School, Issaquah, WA
Allison C., age 12 - Issaquah Middle School, Issaquah, WA
Katharine C., age 12 - Issaquah Middle School, Issaquah, WA
Lisa C., age 13 - Issaquah Middle School, Issaquah, WA
Pam C., age 13 - Issaquah Middle School, Issaquah, WA
Aaron D., age 12 - Issaquah Middle School, Issaquah, WA
David D., age 13 - Issaquah Middle School, Issaquah, WA
Andy E., age 13 - Issaquah Middle School, Issaquah, WA
Karen F., age 14 - Issaquah Middle School, Issaquah, WA
Jackie G., age 13 - Issaquah Middle School, Issaquah, WA
Megan G., age 13 - Issaquah Middle School, Issaquah, WA
Greg H., age 12 - Issaquah Middle School, Issaquah, WA
Jordan H., age 13 - Issaquah Middle School, Issaquah, WA
Phillip H., age 13 - Issaquah Middle School, Issaquah, WA
Witt H., age 12 - Issaquah Middle School, Issaquah, WA
Chris I., age 13 - Issaquah Middle School, Issaquah, WA
Matthew I., age 13 - Issaquah Middle School, Issaquah, WA
Kaitlin J., age 14 - Issaquah Middle School, Issaquah, WA
Lindsay J., age - Issaquah Middle School, Issaquah, WA
Paul J., age 15 - Issaquah Middle School, Issaquah, WA
Ashok K., age 13 - Issaquah Middle School, Issaquah, WA
Jessie K., age 13 - Issaquah Middle School, Issaquah, WA
Kristi K., age 14 - Issaquah Middle School, Issaquah, WA
Darrick L., age 13 - Issaquah Middle School, Issaquah, WA
Amanda M., age 13 - Issaquah Middle School, Issaquah, WA
Kelly M., age 13 - Issaquah Middle School, Issaquah, WA
Sean M., age 13 - Issaquah Middle School, Issaquah, WA
Stacey M., age 12 - Issaquah Middle School, Issaquah, WA
Tyler M., age 14 - Issaquah Middle School, Issaquah, WA
Tani O., age 12 - Issaquah Middle School, Issaquah, WA
Jamin S., age 13 - Issaquah Middle School, Issaquah, WA
Scott S., age 14 - Issaquah Middle School, Issaquah, WA
Vasiliy S., age 13 - Issaquah Middle School, Issaquah, WA
Kaite T., age 13 - Issaquah Middle School, Issaquah, WA
Kasey T., age 13 - Issaquah Middle School, Issaquah, WA
Ella W., age 13 - Issaquah Middle School, Issaquah, WA
Justine W., age 12 - Issaquah Middle School, Issaquah, WA
Kirsten W., age 12 - Issaquah Middle School, Issaquah, WA
Mac W., age 14 - Issaquah Middle School, Issaquah, WA
Matthew W., age 13 - Issaquah Middle School, Issaquah, WA
David Y., age 12 - Issaquah Middle School, Issaquah, WA