Centipede and Bug: Part Two
NAME ___________________
Part 1
One sunny day, Senn T. Pede and his friend Lady Bug start out from the elm tree and move
toward the rose bush, which is 45 feet away. Senn crawls at 5 feet per minute and Lady crawls at
3 feet per minute. However, Lady Bug gets a 4 minute head start.
1. Use the diagram below to show where each critter is as Senn starts after Lady. Place the
letter S at Senn’s location and the letter L at Lady’s location, remembering Lady Bug
gets a 4 min head start.
2. Use the diagram below to show where each critter is 2 minutes after Senn starts after
Lady. Place the letter S at Senn’s location and the letter L at Lady’s location.
3. Complete the following table to show how far Senn and Lady are from the elm tree for
each time value.
4. Write a sentence to describe a pattern you see in the distance values of Lady’s row of the
table.
5. Let t,represent the number of minutes since Senn starts after Lady. Write an expression
in terms of t for Senn’s distance from the elm tree.
6. Write an expression in terms of t for Lady’s distance from the elm tree.
7. What significance does the coefficient of t in your answer to question 6 have in this
problem? Be certain to include appropriate units in your answer.
8. What significance does the constant term in your answer to question 5 have in this
problem? Be certain to include appropriate units in your answer.
9. Create an equation that could be solved to find the value of t for which Senn catches up
with Lady. Explain what each side of the equation means.
10. If Senn leaves the elm tree at 1:00 p.m., what time is it when he catches up with
(overtakes) Lady?
11. How long will it take Lady to reach her home from the spot where Senn catches up with
her?
12. Describe, in words, a situation involving Senn and Lady that could be described by each
of the following equations:

3t + 12 = 2(5t)

92 – 5t = 62
Part 2
Senn and Lady have a turtle friend, Archimedes, who sometimes studies with them. Archimedes
arrived shortly after Senn left to catch up with Lady, and he tried to overtake them to tell them
that the science test had been canceled because the school copy machine had broken down.
13. The following equation describes Archimedes’ attempt to catch up with Senn and Lady.
In this equation, A represents Archimedes’ distance from the elm tree and t represents the
number of minutes since Senn left the elm tree. Describe, in words, what this equation
tells you about Archimedes’ attempt to catch up with them.
A = 6.4t – 7.2
14. The graph below shows the distance each critter is from the elm tree for the first four and
one-half minutes since Senn left the elm tree to catch up with Lady. Label each line to
show which critter’s travels is represented by the line and clearly explain why you have
made each of these associations.
15. Use the graph in #14 to estimate how far apart the critters were from each other three
minutes after Senn left the elm tree. Check your estimates by using appropriate algebraic
expressions.
Part 3
14. A hare challenges a tortoise to a race. The
graph gives information about part of the race.
a.
Who got a head start and how many
minuets head start did that racer get?
b. How far did the racer with the head start go before the second racer started?
c. At what speed does the tortoise travel? Include units.
d. What is the speed of the hare? Include units.
e. How far ahead of the tortoise was the hare 8 minutes since the tortoise started the
race?
f. Give a possible explanation for the change in the hare’s line, eight minutes since the
tortoise started the race.
g. If the patterns in the graph of the race continue to be the same after 12 minutes as
they are for 8 to 12 minutes, and the tortoise finishes the race 16 minutes after he
starts, who wins the race? Explain below.