3-2 Investigation: On the road again
Materials: On the road table, on the road graph, ruler, and calculator
Name: ______________________________ Per ____
Step1: Find each vehicle’s speed in miles per hour.
A green minivan starts at the Mackinac Bridge and heads south for
Flint on Highway 75.
At the same time, a red sports car leaves Saginaw and a blue pickup
truck leaves Flint. The car and the pickup are heading for the bridge.
The minivan travels 72 miles per hour = _________ miles/min
=
The pickup truck travels 66 miles an hour = ______ miles/min.
=
The sports car travels 48 miles an hour = _______ miles/min.
=
Step 2: Write recursive routines to find each vehicles’ distance from Flint at each minute.
Minivan Rule:
Start value = u0 =220 miles away from Flint
Next value = Previous value  1.2 miles
Write
un  un1  1.2
Where
Pickup Rule:
Start value = u0 =________ miles away from Flint
Next value = Previous value __________miles
Write
Sports Car Rule:
un =next value and un 1 =previous value
un  un1 _____________
miles
Start value = u0 =________ miles away from Flint
Next value = Previous value __________miles
Write
un  un1 _____________ miles
Calculator Hint: How to write a recursive formula using your calculator
Minivan
Pickup
Sports Car
Start at 220
Start at ________
Start at ___________
Rule is subtract 1.2
{0,220}
Hit Enter
Rule is _________
{0,
}
Hit Enter
Rule is ____________
{0,
}
Hit Enter
Step 3: Use the On the Road Again Table to fill out the distances each car is away from Flint.
Time
Minutes
Minivan
Miles
Pickup
Miles
Sports Car
Miles
Write the Rule: Write the Rule: Write the Rule:
Subtract 1.2
miles each
minutes
0
u0  220
1
2
3
4
5
6
7
8
9
10
218.8
217.6
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
196
184
172
208
u0 
u0 
11
43
Highway
Distance from
Flint
Step 4: Plot the information from the table for all three vehicles onto a graph. Mark and label
each axis in 10-unit intervals, with time on the horizontal axis and distance on the
vertical axis.
LABEL each graph as either the Minivan, PICKUP or the SPORTS CAR
Step 5: On the graph, do the points for each vehicle seem to fall on a line?
Does it make sense to connect each vehicle’s points in a line?
If so, draw the line. If not, explain why not.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Use your graph and table to find the answers for Steps 6-10
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Step 6: Where does the starting value for each routine appear on the graph?
Minivan
Starting
Value
220
Rule
Subtract
1.2
How does the recursive rule for each routine affect the
points plotted?
The line goes down with 1.2 miles every minute or
the slope of the line is -1.2 miles per minute.
Pickup
Sports
car
Step 7: Describe how the graph of the minivan is different from the graph of either the pickup
truck or Sports Car.
Step 8: Where are the vehicles when the minivan meets the first one headed north?
The minivan meets the _______________ first at around __________ minutes.
These two vehicles are about _________ miles away from Flint when they meet.
Step 9: How can you tell by looking at the graph whether the pickup or the sports car is
traveling faster?
When and where does the pickup pass the sports car?
The pickup passes the sports car at around __________ minutes and is _______
miles away from Flint.
Step 10: Which vehicle arrives at its destination first? How long does it take?
Which vehicle arrives at its destination second? How long does it take?
Which vehicle arrives at its destination last? How long does it take?
Step 11: What assumptions about the vehicles are you making when you answer the
questions in step 10? List at least two assumptions you need to make.
Assumption #1:
Assumption #2:
Step 12: Consider how to model this situation more realistically. What if the vehicles are
traveling at different speeds? What is one driver stops to get gas or a bite to eat?
What if the vehicles’ speeds are not constant? Discuss how these questions affect the
recursive routines, tables of data and their graphs.