This document provides information about time, distance, and speed including key concepts, units of measurement, conversion formulas between units, and formulas to calculate distance, time, and speed given two of the three variables. It includes examples of using the formulas to solve word problems involving trains passing poles and travel between cities. The document emphasizes that speed, time, and distance are important concepts in navigation, athletics, and transportation scheduling.

1. Bombay Cambridge Gurukul
Time, Distance and Speed
MATHEMATICS
STANDARD : VII

2. Contents
 Time, distance and speed – concept
 Units of Measurement
 Conversion
 Important formulae
 Calculate distance using formula
 Calculate time using formula
 Calculate speed using formula
 Word Problems
 Train goes past a pole
 Time, distance and speed in daily life
 Check It Out

3. Time, Distance & SpeedConcept
Home
Tree
In the picture above the girl is going really
fast. She catches up and passes the boy.
Can you say who is slower?
The boy is slower than the girl. Can you
say why is the boy slower than the girl?
The boy is slower than the girl because the
boy
takes more time to cover the same
(Contd…)
distance.

4. We can also say that the speed of boy is
less than that of the girl.
When a person covers a given distance in a
given time then the person is said to be in
motion and the rate with which he/she
moves is called speed.
BACK

5. Units of Measurement
The units of measurement of distance are
km, m, cm etc.
The units of measurement of time are hour (hr),
minute (min), second (sec).
The units of measurement of speed are
km/hr and m/sec, cm/sec etc.
NOTE: The units of time and distance determine
the unit of measurement of speed.
BACK

6. Conversion
1000 m = 1 km
1 km
1m =
1000
1 hr = 60 min
1 min = 60 sec
∴ 1 hr = 60 × 60
sec
∴ 1 sec =
1
60 × 60 hr
(Contd…)

7. 1) Changing the speed given in km/hr into m/sec.
e.g. 90km/hr = 90 x
5
10
= 90 x
5
1000 m
60 x 60 sec
3
5m
18 sec
2
1
90 km/hr = 25 m/sec
(Contd…)

8. 2) Changing the speed given in m/sec into km/hr.
50 km
e.g. 50m/sec =
1000
∴
÷
1
hr
60 x 60
50 x 60 x 60
=
1000
3
50m/sec = 50 x 60 x 60
1000
5
10
18 km
= 50 x
5 hr
1
50m/sec = 180km/hr

9. Easy way to Remember
Conversion
To convert the speed given in km/hr into
m/sec, multiply the given speed by 5
18
To convert the speed given in m/sec into
km/hr, multiply the given speed by 18
5
BACK

10. Important Formulae
DISTANCE = SPEED X TIME
SPEED =
TIME =
DISTANCE
TIME
DISTANCE
SPEED
Easy Way to Remember the Distance Formula:
If you know any of the two of the three variables, (distance,
Ispeed in DSTREET. (DST are what the otheras in the
stay and time) you can find out in the order one is.
Distance Formula.)
BACK

11. I) CALCULATE DISTANCE FROM SPEED AND TIME
Enter Speed
40
m/sec
Enter Time
10
sec
DISTANCE = SPEED
=
=
BACK
X
40 m/sec
400
m
TIME
X
10 sec

12. II) CALCULATE TIME FROM DISTANCE AND SPEED
Enter Distance
30
m
Enter Speed
27
km/hr
Distance & speed are not in the same unit of measurement, so
conversion is required.
Conversion:
Speed = 27km/hr
3
15 m/sec
= 27 x 5 =
2
18
2
( Contd…….)

13. TIME = DISTANCE
SPEED
=
30 m
15/2 m/sec
2
= 30 X
2
= 4 sec.
15
1
TIME = 4 seconds
BACK

14. III) CALCULATE SPEED FROM TIME AND DISTANCE
Enter Time
2 hrs
Enter Distance
45 min
132 km
Time is given in both hour and minute so this can be
converted into hour.
Conversion : Time = 2 hrs 45 min
OR
Time = 2 hrs + 45 min
3
45 min = 45 hr
60 4
( Contd…….)

15. (Contd…….)
45 min =
3 hr
4
∴ 2 hrs + 45 min = 2 hr + 3 hr
4
8 + 3 hr
=
4
= 11 hr
4
(Contd…….)

16. SPEED = DISTANCE
TIME
=
132 km
11/4 hr
12
= 132 X
4
11
1
SPEED = 48 km/hr
BACK

17. Word Problems
The distance between Pune and Nasik is 352 km. A
bus running at the speed of 40 km/hr left Pune at
20.00 hrs. What time will it reach Nasik?
TIME = DISTANCE ÷ SPEED
44
4 hr
4 hrs
44 hrs
352 km
= 8 hrs +
= 8
=
=
5
5
5
40 km/hr
5
12
4 X 60 min
= 8 hrs and
5
1
= 8 hrs and 48 min
The bus started at 20.00 hrs and travelled for a
period of 8 hrs 48 min.
(Contd…)

18. Contd…
∴ the bus reached at 20.00 hrs + 8.48 hrs = 28.48 hrs
To find the time of the day according to the 24 hours
system, let us subtract 24 from 28.48 .
hrs
28
min
48
24
00
4
48
= 4 hrs and 48 min
The bus reached Nasik early morning the
next day at 4 hours and 48 minutes.
BACK

19. TRAIN GOES PAST A POLE
Q. A train running at the speed of 36 km/hr goes
past a pole in 20 seconds. Find the length of
the train.
W does the phrase “train goes past a pole mean”?
hat
This means that the train has to travel a
distance equal to its length to go past
the pole. Hence, the time required to go
past a pole is the same as the time
required to travel a distance equal to the
train’s length.
(Contd…)

20. SOLUTION:
The length of the train will be equal to the
distance travelled in the given time with the
same speed.
Speed = 36 km/hr
Conversion:
Time = 20 sec
2
6
36 km/hr = 36 x 5
= 10 m/sec
18
3
1
DISTANCE = SPEED X TIME
Distance = 10m/sec x 20 sec
BACK
= 200 m

21. Time, Distance and Speed in Daily
Life
Speed, time and distance is one of the basic
tools a sailor uses in navigation. Using these
simple formulae he can predict the time of
arrival, the speed of travel or the distance he
has to cover.
In athletic events and elimination rounds speed,
distance and time play a major role in the
making and breaking of records.
The departure and arrival of aeroplanes, trains
and buses depends on calculations involving
speed, time and distance.
BACK

22. Fill in the blanks and complete the
following:
To convert the speed given in km/hr into m/sec,
multiply the given speed by
1m =
1
km
1000
5
18
60
1 hr = 60 × ______ sec
Speed = Distance
Time
Time =
Distance
Speed
Speed
Distance = ___________ X Time
1 sec =
1
60
60
___ × ___
hr
BACK

23. The End
Created by
Department of R
esearch