Mathematics Powerpoint

1. SPEED,
DISTANCE AND
TIME

2. At the end of this module, you are expected
to:
state the formula in finding the speed,
distance and time;
identify the speed, distance and time in the
given problem;
solve each problem involving speed,
distance and time.

3. Let us analyze and solve this problem.
Mr. Cruz went to the province. He
drove for 2 hours travelling at an
average speed of 80 kilometers
per hour. How far did he travel to
reach the province?

4. How do you solve this problem? Analyze this
problem by using the following guide questions.
1. What is asked in the problem?
The distance that Mr. Cruz travelled.
2. What are given in this problem?
2 hours which refers to time, 80 kilometers
per hour which is the average speed

5. 3. Represent the unknown, using a variable.
Since you are asked to find the distance that Mr.
Cruz traveled, let the variable d represent the
distance traveled.
d = the distance traveled in kilometers
4. Next, relate the given information in the problem to the
unknown number of kilometers by means of an equation.
There is a relationship that exists among
distance, time, and speed.

6. Formulas can be derived
from the triangle in Figure 1.
In the figure, d = distance,
s = average speed, and
t = time.
To find d, multiply the
average speed and the time.
d = s × t

7. To find s, divide the distance by the time.
d
t
To find t, divide the distance by the
average speed.
d
S

8. 5. The equation d = s × t describes the problem.
6. Solve the equation.
d = s × t
= 80 km × 2 hours
hour
= 160 km
Mr. Cruz traveled 160 km to reach the
province.

9. Speed, Distance, and Time Formula
The relationship between speed, distance, and time can be
expressed in the following equations:

10. To further understand the relationship between these three
terms (speed, distance, and time) in the formula, analyze the
situation below.
When we say a track event at the Palarong Pambansa
is500 meters long, we are defining its distance. Yet most
people are interested in the time taken to run it.
Equally, however, we could consider them to run a longer
distance in the same time. Both points of view are exactly the
same. All that we are talking about is their average speed,
which is defined by:

11. Definition of Average Speed
Average speed is a measure of the distance traveled in a given
period of time; it is sometimes referred to as the ratio of distance
and time.
Distance
time
Why is the term average speed used? Think about how the race
happens they start from being at rest, speed up, and run at almost
the same speed throughout.
In everyday life, we use speeds like kilometers per hour (km/h),
whereas in this race we use meter per second (m/s).
Average Speed =

12. Definition of Speed
Speed is a scalar quantity that refers to “how fast an object is
moving.”
Speed can be thought of as the rate by which an object covers
distance.
A fast-moving object has a high speed and covers a relatively
long distance in a short amount of time. Contrast this to a slow-
moving object that has a low speed and covers a relatively
small amount of distance in the same amount of time. An object
with no movement at all has a zero speed.

13. Definition of Distance and Time
Distance is the total length between two positions.
Time is the quantity measured or measurable period during which an
action, process, or condition exists or continues.
The equation for speed can be remembered from the unit itself: m/s–
m is meters (distance),s is seconds (time). It can, of course, be
arranged to give:
distance
speed and distance = speed × time
Time =

14. The following table lists units in common use for speed and their
abbreviations.

15. Example 1:If a car travels 100 kilometers in 2 hours,
find the average speed.
Solution:
Using the average speed formula:
Distance 100
Time 2
Answer: The average speed of the car is 50 kph.
Take note that the car does not travel at a constant
speed of 50 kph; its speed varies during the journey.
Average Speed = = = 50 kph

16. Example 2:A world-record holder ran 800 metersin
86 seconds. What was his average speed rounded
to the nearest tenth?
Solution:
Using the average speed formula:
Distance 800 m
Time 86 s
Answer: The average speed of the world-record
holder was 9.3 m/s
Average Speed = = = 9.3 m/s

17. Example 3:Rey drives at an average of 45
mph on a journey of 135 miles. How long
does the journey would take?
Solution:
Using the average speed formula:
distance 135 miles
time 45 mph
Answer:The journey takes 3 hours.
Average Speed = = = 3 hours

18. Example 4:Wayne’s motorcycle’s average speed on a
motorcycle is 50 km/h. If he drivesit for 4 1/2 hours,
how far does he travel?
Solution:
Using the formula to find the distance:
distance = speed × time
= 50 × 4 1/2
distance = 225 kilometers
Answer: He can travel a distance of 225 kilometers.

19. Example 5: Michael can type 840 words in 20 minutes. Calculate his
typing speed in:
a. words per minute
b. words per hour
Solution:
His typing speed can be calculated as:
a. Typing speed =
In 1 hour we have 60 minutes, so:
b. Typing speed = 42 × 60 = 2 520 words per hour.
20
840
= 42 words per minute

21. Directions: Identify the given data in each problem and the
unknown to be solved. Write your answer on your answer sheet.
1. Jea drove her car at an average speed of 62
kilometers per hour for 3 hours. How far did she go?
D = _____
T = _____
S = _____

22. 2. In how many hours can a cyclist travel 765
kilometers at the rate of 45 kilometers per
hour?
D = _____
S = _____
T = _____

23. 3. In 3 hours, a commuter train traveled
a distance of 135 kilometers. What was
the speed of the train?
T = _____
D = _____
S = _____

24. 4. Wayne bought a new car. He drove his
car from Manila to Baguio City at an average
speed of 65 kilometers per hour, for a total of
4.5 hours. How far did he travel?
S = _____
T = _____
D = _____

25. 5. How long does it take to travel a distance of
672 kilometers at a speed of 96 kilometers per
hour?
D = _____
S = _____
T = _____