1
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.1
TASK 3.4.1: DISTANCE AND TIME
Solutions
Roberto and Juanita own a go-cart racing track. Their go-carts have governors on the
accelerators that prevent them from exceeding 36 mph. The track the go-carts run on is a
2 mile oval. They have decided to charge a flat fee for 36 miles, but they need to know
how long it will take to complete the laps at different speeds.
Complete the table below:
Distance (miles)
Rate (mph)
Process
Time (hours)
36
1
36/1
36
36
2
36/2
18
36
3
36/3
12
36
36
36
4
6
9
36/4
36/6
36/9
9
6
4
36
12
36/12
3
36
18
36/18
36
36
36/36
2
1
D
R
D/R
T
1. What relationships do you observe between the variables distance, time, and rate?
Rate x Time equals distance.
Distance/Time is Rate and Distance/Rate is Time.
2. Given any two of the variables, explain how you would find the third.
Given D and T, D/T = R Given T and R, T·R = D Given D and R, D/R = T
3. Enter the rate data in L1 on your calculator. Enter the time date in L2 on your
graphing calculator. Graph L1 as independent and L2 as the dependent variable.
Sketch the graph on your paper. What are the range and domain for this
situation?
The range for the data is 1 to 36, the domain is also 1 to 36.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
2
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.1
4. Write the symbolic representation for the graph if time is dependent and rate is
independent.
y = 36/x
5. In direct variation, the constant of proportionality is found by dividing the
y
dependent variable by the independent variable
. This task represents an
x
inverse variation. Here the independent variable times the dependent variable
establishes the constant (y * x). Use your graphing calculator to multiply L2
times L1; have the product placed in L3. What is the result?
If you multiply L1 by L2 the result will be 36.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
3
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.1
TASK 3.4.1: DISTANCE AND TIME
Roberto and Juanita own a go-cart racing track. Their go-carts have governors on the
accelerators that prevent them from exceeding 36mph. The track the go-carts run on is a
2 mile oval. They have decided to charge a flat fee for 36 miles, but they need to know
how long it will take to complete the laps at different speeds.
Complete the table below:
Distance (miles)
Rate (mph)
36
1
36
2
36
3
36
36
36
4
6
9
36
12
36
18
36
36
D
R
Process
Time (hours)
1. What relationships do you observe between the variables distance, time, and rate?
2. Given any two of the variables, explain how you would find the third.
3. Enter the rate data in L1 on your calculator. Enter the time date in L2 on your
graphing calculator. Graph L1 as independent and L2 as the dependent variable.
Sketch the graph on your paper. What is the range and domain for this situation?
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
4
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.1
4. Write the symbolic representation for the graph in terms of x and y.
5. In direct variation, the constant of proportionality is found by dividing the
y
dependent variable by the independent variable
. This task represents an
x
inverse variation. Here the independent variable times the dependent variable
establishes the constant (y * x). Use your graphing calculator to multiply L2
times L1; have the product placed in L3. What is the result?
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.