Mathematics 6
Quarter 3
Module 9
Solving Problems Involving Average Rate
and Speed
Math – Grade 6
Quarter 3 – Module 9: Solving Problems Involving Average Rate and Speed
First Edition 2020
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Published by the Department of Education - Schools Division of Pasig City
Development Team of the Self-Learning Module
Writer: Leonille Villa
Editor (Content and Language): Pelilia B. Vela
Reviewers (Content and Language): Wilma P. Soriano and
Teresita P. Tagulao EdD
Illustrator:
Layout Artist:
Management Team: Ma. Evalou Concepcion A. Agustin
OIC-Schools Division Superintendent
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Printed in the Philippines by Department of Education – Schools Division of
Pasig City
Mathematics 6
Quarter 3
Module 9
Solving Problems Involving Average Rate and Speed
Introductory Message
For the facilitator:
Welcome to the Mathematics 6 Self–Learning Module on Solving Problems
Involving Average Rate and Speed
This module was collaboratively designed, developed and reviewed by educators from
Schools Division Office of Pasig City headed by its Officer-In-Charge Schools Division
Superintendent, Ma. Evalou Concepcion A. Agustin in partnership with the Local
Government of Pasig through its mayor, Honorable Victor Ma. Regis N. Sotto.
The writers utilized the standards set by the K to 12 Curriculum using the Most
Essential Learning Competencies (MELC) while overcoming their personal, social,
and economic constraints in schooling.
This learning material hopes to engage the learners into guided and independent
learning activities at their own pace and time. Further, this also aims to help learners
acquire the needed 21st century skills especially the 5 Cs namely: Communication,
Collaboration, Creativity, Critical Thinking and Character while taking into
consideration their needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of
the module:
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to manage
their own learning. Moreover, you are expected to encourage and assist the learners
as they do the tasks included in the module.
For the learner:
Welcome to the Mathematics 6 Self-Learning Module on Solving Problems
Involving Average Rate and Speed
The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner
is capable and empowered to successfully achieve the relevant competencies and
skills at your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning material while being an active learner.
This module has the following parts and corresponding icons:
Expectations - This points to the set of knowledge and skills
that you will learn after completing the module.
Pretest - This measures your prior knowledge about the lesson
at hand.
Recap - This part of the module provides a review of concepts
and skills that you already know about a previous lesson.
Lesson - This section discusses the topic in the module.
Activities - This is a set of activities that you need to perform.
Wrap Up - This section summarizes the concepts and
application of the lesson.
Valuing - This part integrates a desirable moral value in the
lesson.
Posttest - This measure how much you have learned from the
entire module.
EXPECTATION
At the end of the lesson, you are expected to solve problems involving average
rate and speed.
PRETEST
Directions: Choose the letter of the correct answer.
1. Samuel runs 240 meters in 12 seconds. What is his average speed?
A. 18 m/sec B. 20 m/sec C. 22 m/sec D. 24 m/sec
2. A typhoon is moving at the speed of 1 250 km in 10 hours. What is the
average speed of the typhoon?
A. 125 kph B. 130 kph C. 135 kph D. 140 kph
3. Lito drove for 3 hours at a rate of 50 km per hour and for 2 hours at 60 km
per hour. What was his average speed for the whole journey?
A. 50 kph B. 52 kph C. 54 kph D. 56 kph
4. Francis walks 144 meters in 12 minutes from his house to his school.
What is his average speed?
A. 10 meters per minute C. 14 meters per minute
B. 12 meters per minute D. 16 meters per minute
5. Mang Richard, a delivery truck driver, left the warehouse at 9:00 a.m. and
traveled 150 km to reach his destination. What was his average speed if he
arrived at his destination at 11:00 a.m.?
A. 50 kph B. 60 kph C. 65 kph D. 75 kph
RECAP
How do you calculate speed? distance? time?
Directions: Calculate the following:
a. distance = 20 km c. speed = 10 meters per minute
time = 4 hours time = 5 minutes
speed = _______ distance = ____
b. distance = 45 km
speed = 15 kph
time = _________
LESSON
LET’S LEARN
1. A bus took 2 hours to travel 140 km. Find the average speed of the bus.
Distance traveled
Average speed =
Time taken
140
=
2
= 70
The average speed of the bus was
70 km/h.
It traveled 70 km in 1 hour.
Hence, average speed is the total distance divided by the total time for
the trip.
2. AB and BC are two parts of a running track. The length of each part is 60
m.
60 m 60 m
A B C
Angelo ran from Point A to B in 10 seconds. Then, he ran from point B to
C in 15 seconds. What was his average speed?
60
His speed from Point A to B is = 6 m/s .
10
60
His speed from Point B to C is = 4 m/s .
15
Angelo ran at different speeds from A to B and from B to C. To describe
how fast Angelo ran for the whole journey, we need to calculate the average
speed.
The total distance from A to B and from B to C = 60 + 60 = 120 m
The total time Angelo took = 10 + 15 = 25 seconds.
120
Average speed = = 4.8 m/s
25
Therefore, Angelo’s average speed was 4.8 m/s .
1
3. A bus traveled 80 km/h for 1 hours. It then increased its speed and
2
traveled 90 km/h for the next 2 hours. Find the average speed traveled by the
bus.
1
In the first 1 hours, the distance covered is:
2
1 3 240
80 x 1 = 80 x = = 120 km
2 2 2
In the next 2 hours, the distance covered is:
90 x 2 = 180 km
Total Distance = 120 km + 180 km = 300 km
1 1
Total Time = 1 hours + 2 hours = 3 hours
2 2
300 300 2 5
Average speed =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
= 1 = 7 = 300 x = 85
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑜𝑢𝑟𝑠 32 7 7
2
𝟓
The bus travelled with an average speed of 85 kph .
𝟕
ACTIVITIES
Directions: Read, solve and choose the letter of the correct.
1. Ann walked a distance of 176 m to school in 8 minutes. Find her
average speed.
A. 20 m/min B. 21 m/min C. 22 m/min D. 23 m/min
2. Carlo’s home is 360 meters away from his school. It takes him 8 minutes
of walk to reach his school on time. What is his average speed?
A. 45 m/min B. 50 m/min C. 55 m/min D. 60 m/min
3. A horse can run 7 200 meters in 1 200 minutes. What is its average speed?
A. 5 m/min B. 6 m/min C. 7 m/min D. 8 m/min
Keep Practicing
Directions: Read, analyze and solve.
1. At 8:30 a.m., Amelia started cycling from home to school via the library.
She reached school at 8:46 a.m. What was her average travel time?
1
2. Mr. Mendoza drove from Town A to Town B. He covered 3 of the journey in
the first 2 hours. Then, he finished the remaining 210 km in 3 hours. What
was the average speed for the whole journey?
Test Yourself
Directions: Solve the given problems.
1. An express bus travelled 560 km in 7 hours. Find the average speed of the
bus.
2. A ship left at the port at 9:00 p.m. and arrived at the next port at 5:00 a.m.
the next day. The distance between the 2 ports was 200 km. Find the average
speed of the ship.
WRAP UP
What is the formula in finding the average speed and rate?
VALUING
How do you go to school?
If you walk in going there, how fast do you walk?
If you ride in a vehicle, how fast is your travel time?
Why is it important to be on time?
POSTTEST
Directions: Choose the letter that corresponds to the correct answer.
1. A truck took 4 hours to travel 280 km. Find the average speed of the bus?
A. 74 km/h B. 70 km/h C. 66 km/h D. 62 km/h
2. Leo traveled 595 km for 7 hours by a car. What was the average speed of
his journey?
A. 80 kph B. 85 kph C. 90 kph D. 95 kph
3. A ship traveled 770 km for 14 hours. Find the average speed traveled by
the ship.
A. 55 km/h B. 65 km/h C. 70 km/h D. 75 km/h
4. On his first 2 hours of journey, a motorist drove 130 km. For the next 3
hours, he drove 210 km. What was his average speed for the whole journey?
A. 68 km/h B. 78 km/h C. 88 km/h D. 98 km/h
5. A train left Town A going to Town B at 9:30 a.m. It reached its destination
at 12:00 noon. The distance from Town A to Town B is 190 km. What was
the train’s average speed.
A. 75 km/h B. 76 km/h C. 77 km/h D. 78 km/h
KEY TO CORRECTION
REFERENCES
http://www.hitbullseye.com/Quant/Time-and-Distance.php
http://brilliant.org/wiki/speed-distance-and-time/
http://www.softschool.com/formulas/physics/distance_speed_time_formul
a/75/
http://www.math-only-math.com/relationship-between-speed-distance-
and-time.
Villamayor Adela C. et. Al. (2017) Math for life 6, Revised Edition. Manila: Rex
Book Store, Inc.
Ching The P. et. Al. (2016) Primary Mathematics 6, Revised Edition. Manila:
Rex Book Store, Inc.
Burgos Jaime R. et. Al. (2016) 21st Century Mathletes 6. Araneta Avenue,
Quezon City: Vibal Group, Inc.
