Answer Key • Lesson 4: Distance vs. Time
Student Guide
Distance vs. Time (SG pp. 230–233)
Questions 1–18
1–3.* Estimates will vary. Ask students to explain
how they arrived at their estimates.
Explanations for distance traveled on a
one-hour walk might include: I walked for
5 minutes, measured the distance, and
multiplied by 12.
4.* A sample picture is provided in the Student
Guide. If your class uses a different setup, check
that students’ pictures accurately describe the
setup. Make sure the variables are labeled.
5. A.* distance and time
B.* It should be the same walker for all trials.
The walker should walk at the same pace
throughout the experiment, and the timers
should stop their watches when the walker’s
front foot touches or crosses their marks.
6.*See Figure 1 in the lesson for sample data.
7–9.* See Figure 2 in the lesson for sample graphs.
Distance vs. Time
1. If you walk at a steady pace for one hour, how far
can you walk?
2. If you walk at a steady pace, how long does it take
you to walk a mile?
3. What can you measure that will help you answer
these questions?
To find out how fast someone or something is moving, we
measure speed. To measure speed, consider both time and
distance. Speed is the ratio of distance to time. So, speed can be written as a
fraction:
tance moved
ᎏᎏ
Speed = Dis
Time taken
In this experiment, you will measure the time it takes one of your classmates to walk
three different distances so that you can find his or her walking speed. One way to
do the experiment is described here. Your class may need to use a different setup.
230
SG • Grade 5 • Unit 5 • Lesson 4
Copyright © Kendall Hunt Publishing Company
Since speed involves both distance and time, the unit of measure involves both as
well. Speed is measured in miles per hour, meters per second, or feet per second,
and so on. For example, if a car travels 55 miles in one hour, the speed of the car is
55 miles
ᎏᎏ or 55 mph. If a toy car travels 6 meters in 2 seconds,
1 hour
6 meters
ᎏ
the speed of the toy car is 2ᎏ
seconds which is
3 meters
ᎏ
equivalent to 1ᎏ
second .
Distance vs. Time
Student Guide - Page 230
Materials
You will need the following materials for your group:
chalk or tape
meterstick with inches or a yardstick
three stopwatches
Distance vs. Time Data Table in the Student Activity Book
Centimeter Graph Paper
6. A. Use the Distance vs. Time Data Table in the Student Activity Book to record
your data. Repeat the procedure three times and record the results of all
three trials.
B. Find the average time for each distance to the nearest second.
Use the median as your average.
Lab Setup
Distance vs. Time
D
Distance
(in yards)
T
Time (in seconds)
Trial 1
Trial 2
Trial 3
Ordered
Pairs
Average
(Time , Distance)
• Three members of the group will be timers. Another member will be the walker.
One timer should stand near the 6-yard mark, one timer should stand near the
9-yard mark, and one timer should stand near the 12-yard mark.
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• The walker should begin walking at a steady pace several feet behind the
starting line. When the walker crosses the starting line, he or she should say,
“Go.” At that moment, all three timers begin their stopwatches. When the
walker’s front foot touches or crosses each mark, the timer at that marker
stops his or her stopwatch. (Practice once or twice with your group before
you begin recording your data.)
7. Make a point graph of your data. Graph time ( T ) on the horizontal axis and
distance (D) on the vertical axis.
8. What were the measurements for time and distance when the walker crossed
the starting line? (When D = 0 yds, T = ? sec.) Add this point to your graph.
9. If your points lie close to a line, use a ruler to draw a best-fit line. The
best-fit line is the line that is as close as possible to each point.
4. Draw a picture of your setup. Be sure to label the variables with symbols.
Copyright © Kendall Hunt Publishing Company
Copyright © Kendall Hunt Publishing Company
• Measure a straight track that is
12 yards long. With chalk or
tape, mark the beginning and
end of the track. Also mark
points that are 6 yards and
9 yards from the starting line.
(Remember, a yard is
36 inches.)
5. A. What variables will you measure in this experiment?
B. What variables are held fixed? Fixed variables are variables that stay
the same during the whole experiment so that the only thing that affects
the “time taken” is the distance walked.
Distance vs. Time
Student Guide - Page 231
SG • Grade 5 • Unit 5 • Lesson 4
232
231
SG • Grade 5 • Unit 5 • Lesson 4
Distance vs. Time
Student Guide - Page 232
*Answers and/or discussion are included in the lesson.
TG • Grade 5 • Unit 5 • Lesson 4 • Answer Key 1
Answer Key • Lesson 4: Distance vs. Time
10. A. Describe the graph. What does the graph tell you about the relationship
between time and distance?
B. How would a change in time
affect distance?
C. How would a change in
distance affect time?
11. Use your graph to find the time
taken to walk 8 yards.
The answers to Questions 10–18 will vary. Those
provided here are based on Sample Data Tables A and
B and Sample Graphs A and B in Figures 1 and 2 in
the lesson.
10.* A. Answers may include: The best-fit line goes
up at a steady rate; the longer I walk the more
distance I cover.
B. If I took more time, my distance would be
greater; if I walked for less time, my distance
would be less.
12. Find the distance walked after
10 seconds.
A. Give your answer in yards.
B. Give your answer in feet.
C. It would take me longer to walk farther; it
would take less time if I walked a shorter
distance.
11.* Sample Graph A: 5 21 seconds;
13. A. Choose a point on the line
and use it to write the
walker’s speed as a ratio of
distance traveled to time
taken written as a fraction.
B. Choose two more points on the line and use them to write two ratios
equal to the ratio in Question 13A.
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14. A. How many yards did the walker travel in one second?
B. Give the walker’s speed in yards per second (yards/second).

Sample Graph B: 4 32 seconds
12. A.* Sample Graph A: 15 yards;
Sample Graph B: 16 32 yards
15. A. How many feet does the walker travel in one second?
B. Give the walker’s speed in feet per second (feet/second).
Check-In: Question 16
16. If the walker in your experiment
continues at the same pace for one
hour, about how far will he or she
walk? Show or tell how you used
your data to answer the question.
How many seconds
in an hour?
17. Do you think the walker can walk at the same speed you calculated in
Questions 14 and 15 for one hour or longer? Why or why not?
18. There are 5280 feet in a mile. About how many miles can the walker walk in
one hour. How do you know?
Distance vs. Time
SG • Grade 5 • Unit 5 • Lesson 4
233
B.* Sample Graph A: 45 feet;
Sample Graph B: 50 feet
13 A.* Answers may vary.
3 yards
—;
Sample Graph A: DT ——
2 seconds
—
Graph B: DT ——
3 seconds
5 yards
Student Guide - Page 233
B.* Answers based on 13A.
15 yards
9 yards
— ; DT ——
—;
Sample Graph A: DT ——
10 seconds
6 seconds
B.* Sample Graph A: 1.5 yards/second;
Sample Graph B: 1.67 yards/second
15. A.* Sample Graph A: 4.5 feet;
Sample Graph B: 5 feet
B.* Sample Graph A: 4.5 feet/second;
Sample Graph B: 5 feet/second
16.* Answers should demonstrate students’
understanding that they have to go from seconds
to minutes to hours to arrive at their answer.
Sample Graph A: about 16,200 feet or about
5400 yards; Sample Graph B: about 18,000 feet
or about 6000 yards
17.* Answers will vary. Possible response: No. The
walker may get tired. If his or her path goes
uphill, the walker may slow down.
18. A little more than 3 miles; Possible response:
Based on the data in Graph A and the
calculations for Question 16, a little more than
3 miles because 5000 3 15,000 feet.
*Answers and/or discussion are included in the Lesson.
2
TG • Grade 5 • Unit 5 • Lesson 4 • Answer Key
Copyright © Kendall Hunt Publishing Company
15 yards
10 yards
— ; DT ——
—
Graph B: DT ——
9 seconds
6 seconds
14. A.* Graph A: 1.5 yards;
Sample Graph B: 1 32 yards
Answer Key • Lesson 4: Distance vs. Time
Homework (SG pp. 234–235)
Questions 1–13
1. 3 miles
2. 50 minutes
3. A. Answers will vary. One possible ratio is:
Felicia biked for one hour on a bike path. She biked at the same speed for the
entire time. The graph shows her speed.
1. How far did Felicia travel after 15 minutes?
.
2. How long did it take Felicia
to bike 10 miles?
B. Answers will vary. Two possible ratios are:
4.
6.
7.
8.
9.
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10.
11.
12.
13.
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Bicycle Speed
Copyright © Kendall Hunt Publishing Company
5.
3 miles
and 15 minutes .
18 miles; Strategies will vary. Students might
find out how far Felicia can bike in 1 hour
(12 miles), then take half (6 miles) and add it on.
80 minutes or 1 hour and 20 minutes; Strategies
will vary. Students can double the time it takes
her to travel 8 miles.
A. 12 miles
B. 12 miles per hour
195 miles
3 hours
Using mental math:
1000 10 100 and 1000 20 50,
so 1000 15 is about 75 gallons.
Using a calculator:
1000 15 66.666667 or about 67 gallons.
5 hours
6 hours and 15 minutes
A. Ana ate 32 of the pie, which is the most.
Possible strategy using benchmarks: 61 and 52
are less than 21 since the numerators are less
than half the denominators. 32 is greater than 21
since the numerator is more than half the
denominator. So 32 is the largest fraction.
B. Felicia ate 61 of a pie, which is the least. 61 is
the smallest fraction since it is close to zero, 52
is close to 21, and 32 is greater than 21 .
A. Arti lost the most pencils.
B. Manny lost the least number of pencils.
2 miles
10 minutes
3. A. Choose a point on the
graph and use it to
write Felicia’s speed
as a ratio of distance
traveled to time taken.
(Include units.)
B. Write two more ratios
equal to the ratio in
Question 3A.
0 5 10 15 20 25 30 35 40 45 50 55 60
4. If Felicia biked at the same speed for 1ᎏ12ᎏ hours,
how far would she travel?
Explain how you know.
5. The bike path is 16 miles long. If Felicia biked the
entire path at the same speed, how long did she
travel? Explain how you know.
6. A. How far did Felicia travel in one hour?
B. Give Felicia’s speed in miles per hour.
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SG • Grade 5 • Unit 5 • Lesson 4
Distance vs. Time
Student Guide - Page 234
Speedy Problems
Use appropriate tools to solve the following problems.
7. A salesperson has to drive 500 miles. For the first three hours she drove at
65 miles per hour. For the next two hours she drove at 55 miles per hour.
How many more miles does she have left to drive?
8. John bicycles for 2 hours at a speed of
15 miles per hour. How many hours
will it take Shannon to cover the same
distance at a speed of 10 miles per
hour?
9. A truck driver drives 1000 miles. The
truck uses a gallon of diesel fuel for
every 15 miles. About how many
gallons of fuel are needed?
10. One Earth Day, four workers planted
500 white pine seedlings. Each worker could plant 25 trees an hour. How
many hours did it take to plant all 500 trees?
11. A teacher wants to interview
each of his students. He needs
15 minutes for each interview.
How long will it take him to
interview all 25 students in his
class in hours and minutes?
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1 mile
5 minutes
Felicia’s Bike Trip
12. Alexis, Ana, and Felicia each ate fractions
of pie for dessert. Alexis ate 25ᎏᎏ of a pie.
Ana ate 23ᎏᎏ of a pie. Felicia ate 16ᎏᎏ of a pie.
A. If all the pies were the same size,
who ate the most pie? Explain.
B. Who ate the least pie? Tell how
you know.
13. Lin, Manny, and Arti each bought the same size box of pencils.
One month later, 38ᎏᎏ of Lin’s pencils are missing. ᎏ18ᎏ of Manny’s pencils
are missing. ᎏ58ᎏ of Arti’s pencils are missing.
A. Who lost the most pencils?
B. Who lost the least number of pencils?
Distance vs. Time
SG • Grade 5 • Unit 5 • Lesson 4
235
Student Guide - Page 235
TG • Grade 5 • Unit 5 • Lesson 4 • Answer Key 3