#### A Math Forum Project

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

Student Version

### Earthquake 2 - posted February 8, 2000

Try Earthquake 1 before you do this problem.
When their teacher gives the okay, Sally and Suzie (who rides more slowly) hop on their bikes at school and ride to the emergency shelter, passing a house along the way.

1. Explain the meaning of the red, purple, and green lines, as well as the red line segment described above.

2. Suppose that Suzie passes the house 10, 20, or 40 minutes later than Sally. Read the graph to find out how far the house was from the school in each case.

3. (Bonus) Write an expression (a distance, rate, time function) that allows Sally to find out how far the house was from the school, if she knows only the time difference between when she and Suzie passed the house. Please explain how you came up with the expression.

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Students did not completely respond to all of the parts of question 1. Many skipped explaining the "red line segment." Since this was vital to understanding the complete problem, it was necessary for the mentors to point this out and have the students revise and add their thoughts. Occasionally, when the other answers obviously pointed out that the students understood the red line segment's significance, the answer was counted as correct even if they skipped that one part of question 1.

Often students did not seem to draw on their experiences with Earthquake 1 to respond to Earthquake 2. This was evident because they should have started using the term "rate" or "speed," and instead they were still using a more indirect description of that concept.

Students had difficulty seeing the "2.5" value. It might have been helpful to ask questions in decreasing values because it was easier to see the 10 miles for a difference of 40 minutes and the 5 miles for a difference of 20 minutes than it was to see the 2.5 miles for a difference of 10 minutes.

Once students got those exact pairs of numbers, they could see the relation and come up with an answer for the bonus question. It was common, however, for them to use the equation d = 4x rather than d = 1/4x. Students had difficulty transitioning between the different forms of d=rt. (In other words, they were less familiar with r=d/t and t=d/r.)

As was pointed out in the comments on Earthquake 1, the use of the term "expression" in the bonus question should have been "equation." This would have been less confusing.

### Highlighted solutions:

 From: Christina R., age 13Yusra S., age 13 School: Issaquah Middle School, Issaquah, WA

```Page Week 2
1. Explain the meaning of the red, purple, and green lines, as well as the red
line segment described above:

The red line is how the distane Sally and Suzie have traveled. The purple line
Suzie's rate of riding. The green line is the rate of Sally's riding. The red
line segment described above represents the diffrence of rate between the two
girls.

2. Suppose that Suzie passes the house 10, 20, or 40 minutes later than Sally.
Read the graph to find out how far the house was from the school in each case:

10 minutes: 2.5 miles
20 minutes: 5 miles
40 minutes: 10 miles

3. (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to find out how far the house was from the school, if she knows only the
time difference between when she and Suzie passed the house. Please explain
how you came up with the expression.

d=distance       r=rate      t=time
d=rt
2.5=r10
r=1/4
5=r20
r=1/4
10=r40
r=1/4

d=1/4t
So after substituting the distance and time into the d=rt equation we found
that ther was a 1/4 rate. So r=1/4.

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

 From: Brian Y., age 14 School: Issaquah Middle School, Issaquah, WA

```Page Week 2
1. Explain the meaning of the red, purple, and green lines, as well as the red
line segment described above:
red one is how far house is from school, purple one is sally's rate and greeen
one is suzy's rate.
the red line between the gren and purple is the amount of time faster sally is
than suzy

2. Suppose that Suzie passes the house 10, 20, or 40 minutes later than Sally.
Read the graph to find out how far the house was from the school in each case:
10 minutes is 2.5 miles,  20 miutes if 5 miles, and 40 minutes is 10 miles.

3. (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to find out how far the house was from the school, if she knows only the
time difference between when she and Suzie passed the house. Please explain
how you came up with the expression.
time divided by 4= distance in miles. the paterns in number 4 all equaled four
(10/4=2.5, 20/4=5 and so on
------------------------------------
```

 From: Kirsten W., age 12Ella W., age 13 School: Issaquah Middle School, Issaquah, WA

```Page Week 2
1. Explain the meaning of the red, purple, and green lines, as well as the red
line segment described above:

The red line shows the distance that the house is from the school.  The
purple is the rate at which sally rides.  The green line represents suzi's
rate.  The red line segment shows the difference in time that it takes for
suzi and sally to reach the house.

2. Suppose that Suzie passes the house 10, 20, or 40 minutes later than Sally.
Read the graph to find out how far the house was from the school in each case:

10= the house is 2.5 miles from the school.
20= the house is 5 miles from the school.
40= the house is 10 miles from the school.

3. (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to find out how far the house was from the school, if she knows only the
time difference between when she and Suzie passed the house. Please explain
how you came up with the expression.

The time difference divided by 4 equals the distance the house is from the
school.
t divided by 4= D

We looked for patterns in #2 and found that distance in miles is 1/4 of
the time difference.
------------------------------------
```

### 32 students received credit this week.

Alex B., age 12 - Issaquah Middle School, Issaquah, WA
Amber B., age 13 - Issaquah Middle School, Issaquah, WA
Christine B., age 13 - Issaquah Middle School, Issaquah, WA
Jeff B., age 13 - Issaquah Middle School, Issaquah, WA
Keturah B., age 13 - Frisbie Middle School, Rialto, CA
Marissa B., age 13 - Issaquah Middle School, Issaquah, WA
Allen C., age 12 - Issaquah Middle School, Issaquah, WA
Allison C., age 12 - Issaquah Middle School, Issaquah, WA
Jack C., age 13 - Issaquah Middle School, Issaquah, WA
Katie C., age 13 - Issaquah Middle School, Issaquah, WA
Katie D., age 13 - Issaquah Middle School, Issaquah, WA
Chris G., age 14 - Issaquah Middle School, Issaquah, WA
Bryant H., age 13 - Frisbie Middle School, Rialto, CA
Phillip H., age 13 - Issaquah Middle School, Issaquah, WA
Katelyn J., age 13 - Issaquah Middle School, Issaquah, WA
Ashok K., age 13 - Issaquah Middle School, Issaquah, WA
David L., age 13 - Issaquah Middle School, Issaquah, WA
Derek L., age 13 - Issaquah Middle School, Issaquah, WA
Sean M., age 13 - Issaquah Middle School, Issaquah, WA
Christina R., age 13 - Issaquah Middle School, Issaquah, WA
Sean R., age 13 - Issaquah Middle School, Issaquah, WA
Jayna S., age 14 - Issaquah Middle School, Issaquah, WA
Matt S., age 13 - Issaquah Middle School, Issaquah, WA
Paradie S., age - Issaquah Middle School, Issaquah, WA
Scott S., age 14 - Issaquah Middle School, Issaquah, WA
Yusra S., age 13 - Issaquah Middle School, Issaquah, WA
Jesse T., age 13 - Issaquah Middle School, Issaquah, WA
Johanna T., age 14 - Issaquah Middle School, Issaquah, WA
Ella W., age 13 - Issaquah Middle School, Issaquah, WA
Kirsten W., age 12 - Issaquah Middle School, Issaquah, WA
Matthew W., age 13 - Issaquah Middle School, Issaquah, WA
Brian Y., age 14 - Issaquah Middle School, Issaquah, WA