#### A Math Forum Project

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

Student Version

### Earthquake 1 - posted February 1, 2000

Near the end of Sally's school day, a minor earthquake occurs. Soon the "all clear" is given and it is safe to go home. Sally rides her bike at the rate shown in the graph.

1. Explain the meaning of the red line, the purple line, and the horizontal and vertical axes on the graph.

2. Suppose that Sally's home is either 3, 7, or 10 miles from school. Move the slider and read the graph to find out how long it takes her to get home in each case. How do you know?

3. (Bonus) Write an expression (a distance, rate, time function) that allows Sally to figure out how long it will take her to ride her bike from school to any home location. Explain how you came up with the expression.

If you are not using the Escot Runner, you must use it to work on this problem.
Other browsers will not display Escot activities

If you are using the Escot Runner, you may use the link below to download and try this problem.
Want to try it?

Students seemed to have a few difficulties with this set of questions. The meaning of the purple line was not obvious to them, and they often used the readouts of the time for question 2 instead of reading the graph. The term "expression" also confused them; what we were actually looking for was an "equation."

For question 2, we wanted them to read the graph, but we provided them with a readout. Some of them realized that if you lined the boxes up from Sally and the house, the readout was perfect. It was very difficult, however, to motivate those who got the answer that way to tell us how to read the graph, but that was what we were requiring them to do.

As a modification to this problem in the future, we would not provide the readout and we would make sure that the graph gave precise numbers, so students could figure out the rate.

### Highlighted solutions:

 From: Bryant H., age 13 School: Frisbie Middle School, Rialto, CA

```Page Week 1

1) Explain the meaning of the red line, the purple line, and the horizontal
and vertical axes on the graph.the red line shows  how many miles is her
school from her house the purple show the rate of the time it takes her to get
to her house, and the horizontal line  shows the total possible minutes. The
vertical axes shows the total possible mile.
2) Suppose that Sally's home is either 3, 7, or 10 miles from school. Movee
slider and read the graph to find out how long it takes her to get home in
each case. How do you know? if her house was three miles away it would take
her 18 minutes to get home,if  she was seven miles from home it would take her
42 minutes to get home, and if she was ten miles from home it would take her
60 minutes to get home.because I move her and match the purple square with the
red square that is how I got my answer.
3) (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to figure out how long it will take her to ride her bike from school to
any home location. Explain how you came up with the expression.
My expression for Sally to show her how to get to any location is to tell her
that she need to use a formula like d= r x t to show her how she will know to
get to her location or she can get a stopwatch and to know how many miles she
is from her school and to time herself.

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

 From: Lindsay J., age Alison L., age School: Issaquah Middle School, Issaquah, WA

```Page Week 1

1) Explain the meaning of the red line, the purple line, and the horizontal
and vertical axes on the graph.

The red line is the distance she travels.
The vertical axes measures the miles she must travel to go home.
The horizontal axes measures the time she takes to get home.
The purple line is the rate she rides her bike.

2) Suppose that Sally's home is either 3, 7, or 10 miles from school. Move the
slider and read the graph to find out how long it takes her to get home in
each case. How do you know?

3 miles- The red and purple line intersect at 18 minutes so thats how long it
takes her to get home.
7 miles- The red and purple line intersect at 43 minutes so thats how long it
takes her to get home.
10 miles- The red and purple line intersect at 60 minutes so thats how long it
takes her to get home.

3) (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to figure out how long it will take her to ride her bike from school to
any home location. Explain how you came up with the expression.

d=r*t (distance=rate*time)
The distance is "d" because it is any given distance.
3=r*.3  7=r*.716    10=r*1
The rate is 10 miles an hour because it takes her i hour to go 10 miles.
The time is what we need to find out so it is "y."
The new expression is y=d/10
------------------------------------
```

 From: Sean M., age 13 School: Issaquah Middle School, Issaquah, WA

```Page Week 1

1) Explain the meaning of the red line, the purple line, and the horizontal
and vertical axes on the graph.

The red line is the distance between the house and the school.
The Purple line is the rate at which Sally travels
The X-axis is the time
The Y-axis is the distance

---------------------------------------------------------------------
2) Suppose that Sally's home is either 3, 7, or 10 miles from school. Move the
slider and read the graph to find out how long it takes her to get home in
each case. How do you know?

3 miles: 18 minutes
7 miles: 42 minutes
10 miles: 60 minutes

I know this because the purple, red, and grey lines all intersect a
each of these points.

--------------------------------------------------------------------
3) (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to figure out how long it will take her to ride her bike from school to
any home location. Explain how you came up with the expression.

Sally's Speed = 10mph
T = Time in hours
D = Distance in Miles

D=RT
---------------------EXPRESSION-------------------
T= D/10
(Time = Distance divided by 10)

-------------------EXPLANATION-------------------
Since distance eqals rate times time (D=RT), we solved for "T" and  got T=D/R
(time = distance divided by rate).  We then substituted 10mph for the rate and
got T=D/10
------------------------------------
```

 From: Chris F., age 14 School: Issaquah Middle School, Issaquah, WA

```Page Week 1

1) Well, the red line on the graph represents the house. It displays the
number of miles it is away from the school and the amount of miles it can
travel in a given time. The purple line represents Sally. It displays how many
miles she can bike in a certain ampount of minutes. Also, the slope of the
purple line represents her speed. The vertical line is the number of miles for
either line. The horisontal line represents the number of minutes it takes for
the person or home to get a certain amount of miles.
2)I know Sally is home because on the graph, when the lines meet, that means,
that if they are on a straight line that they both would have reached each
other in that point of time. In this case, Sally has reached her home at the
point where the two lines meet.
3) (BONUS) X= the number of miles. Y= the amount of time iot takes her to
complete her journey home.
Y= 6x

I tested how long it would take Sally to get one mile by moving the home
one mile from the school she goes to. Then, I stoped the vertical line that
moves across the screen when it ended up right over where the two lines meet.
The analysis of the line in the bottom- right-hand corner said 6 minutes. So,
for each mile Sally has to go at a constant rate of 10 miles per hour, then
the formula for the amount of time it takjes her is 6x=Y
------------------------------------
```

 From: Keturah B., age 13 School: Frisbie Middle School, Rialto, CA

```Page Week 1

1) Explain the meaning of the red line, the purple line, and the horizontal
and vertical axes on the graph.

The red line shows  the number of miles from Sally's school to her house.  The
purple line shows the rate, or how long it takes Sally to get from her school
to her house.  The horizontal axes shows the possible nuber of minutes it can
take her to get from her school to her house.  The vertical axes shows the
possible miles.

2) Suppose that Sally's home is either 3, 7, or 10 miles from school. Move the
slider and read the graph to find out how long it takes her to get home in
each case. How do you know?

If her Sally's house is 3 miles from her school it will take her 18 minutes.
When I set vertical axes on 7 miles I found out that it would take her 42
minutes.  Then I set the miles on 10 and I found out it would take her 60
minutes or one hour.  I know these times are right, because if you move the
slider where the two lines meet and you get the time.

3) (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to figure out how long it will take her to ride her bike from school to
any home location. Explain how you came up with the expression.

I found the expression distance=rate*time.  This is how I found it.  First I
looked at the minutes it took her to get to each location.  I noticed that if
you multiply each number of miles by 6 you will come up with the minutes.
When I checked it  found out that you have to multiply the minutes by 1/6,
when you do that you will get the miles.  By doing the problem this way I was
able to figure out that she travels 1 mile every 6 minutes.  I also figured
out two more ways of saying the rate Sally travels at.  One way is: Sally
rides her bike at a rate of 1/6 mile per minute.  The other way is: Sally
rides her bike 1/6 mile every one minute.
------------------------------------
```

 From: Allen C., age 12 School: Issaquah Middle School, Issaquah, WA

```Page Week 1

1) Explain the meaning of the red line, the purple line, and the horizontal
and vertical axes on the graph.

The red line stands for the distance between the house and the school, the
purple is the distance to time ratio, the x axis stands for the time it takes
to ride from the school to the house, and the y axis stands for the distances
that are possible between the two buildings.

2) Suppose that Sally's home is either 3, 7, or 10 miles from school. Move the
slider and read the graph to find out how long it takes her to get home in
each case. How do you know?

For 3 miles, it is about 17 minutes. For 7 miles, it is about 42 minutes. For
10 miles, it is 1 hour. I know this because what I have to do is slide the red
line to the appropriate distance and see what time the red and purple line
intersect.

3) (BONUS) Write an expression (a distance, rate, time function) that allows
Sally to figure out how long it will take her to ride her bike from school to
any home location. Explain how you came up with the expression.

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

### 67 students received credit this week.

Jared A., age - Issaquah Middle School, Issaquah, WA
Mark A., age 13 - Frisbie Middle School, Rialto, CA
Reina A., age 13 - Frisbie Middle School, Rialto, CA
Sarah A., age 14 - Issaquah Middle School, Issaquah, WA
Alex B., age 12 - Issaquah Middle School, Issaquah, WA
Amy B., age 13 - Issaquah Middle School, Issaquah, WA
Andrew B., age 13 - Issaquah Middle School, Issaquah, WA
Christine B., age 13 - Issaquah Middle School, Issaquah, WA
Eric B., age 13 - Issaquah Middle School, Issaquah, WA
Jeff B., age 13 - Issaquah Middle School, Issaquah, WA
Jessie B., age 13 - Frisbie Middle School, Rialto, CA
Keturah B., age 13 - Frisbie Middle School, Rialto, CA
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
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
Jamecia C., age 13 - Frisbie Middle School, Rialto, CA
Jonathan (Jon) C., age 13 - Issaquah Middle School, Issaquah, WA
Katharine C., age 12 - Issaquah Middle School, Issaquah, WA
Andrew D., age 14 - Issaquah Middle School, Issaquah, WA
Buddy D., age 12 - Issaquah Middle School, Issaquah, WA
North E., age 13 - Issaquah Middle School, Issaquah, WA
Consuelo G., age 13 - Frisbie Middle School, Rialto, CA
Bryant H., age 13 - Frisbie Middle School, Rialto, CA
Greg H., age 12 - Issaquah Middle School, Issaquah, WA
Jason H., age 14 - Issaquah Middle School, Issaquah, WA
Jordan H., age 13 - Issaquah Middle School, Issaquah, WA
Phillip H., age 13 - Issaquah Middle School, Issaquah, WA
I., average age 13 - Issaquah Middle School, Issaquah, WA
Lindsay J., age - Issaquah Middle School, Issaquah, WA
Octavius J., age 13 - Frisbie Middle School, Rialto, CA
Albert K., age 12 - Issaquah Middle School, Issaquah, WA
Ashok K., age 13 - Issaquah Middle School, Issaquah, WA
La Shanette K., age 13 - Frisbie Middle School, Rialto, CA
Richa K., age 13 - Issaquah Middle School, Issaquah, WA
Thomas K., age 14 - Issaquah Middle School, Issaquah, WA
Alison L., age - Issaquah Middle School, Issaquah, WA
Bryan L., age 13 - Issaquah Middle School, Issaquah, WA
Courtney L., age 13 - Issaquah Middle School, Issaquah, WA
Carly M., age 13 - Issaquah Middle School, Issaquah, WA
Leslie 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
Kristina N., age 12 - Issaquah Middle School, Issaquah, WA
Kathy R., age 13 - Frisbie Middle School, Rialto, CA
Rachel R., age 13 - Issaquah Middle School, Issaquah, WA
Sarah R., age 14 - Issaquah Middle School, Issaquah, WA
Sean R., age 13 - Issaquah Middle School, Issaquah, WA
Holly S., age 14 - Issaquah Middle School, Issaquah, WA
Jayna S., age 14 - Issaquah Middle School, Issaquah, WA
Matt S., age 13 - Issaquah Middle School, Issaquah, WA
Norma S., age 13 - Frisbie Middle School, Rialto, CA
Scott S., age 14 - Issaquah Middle School, Issaquah, WA
Vasiliy S., age 13 - Issaquah Middle School, Issaquah, WA
Johanna T., age 14 - Issaquah Middle School, Issaquah, WA
Kasey T., age 13 - Issaquah Middle School, Issaquah, WA
Sei T., age 12 - Issaquah Middle School, Issaquah, WA
Alicia W., age 13 - Frisbie Middle School, Rialto, CA
Andrew W., 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
Matthew W., age 13 - Issaquah Middle School, Issaquah, WA
Devon Y., age - Issaquah Middle School, Issaquah, WA