1. The document provides teaching notes on speed, time, and distance concepts including definitions of key terms like speed, average speed, and relative speed. 2. It includes examples of speed, time, and distance word problems and step-by-step solutions showing calculations and conversions between units. 3. Sample problems cover topics like calculating time to meeting points, average speeds, relative speeds of objects traveling in the same or opposite directions, and speed of boats traveling upstream or downstream.

1. 2IIM
Ascent Education’s
An IIM Alumni Venture
Speed Time
Teaching Notes – 2IIM

2. 2IIM
Ascent Education’s
An IIM Alumni Venture
Theory
Speed Time Distance - Basic concepts
2
Speed =
Kindly make sure that the units used are consistent.
1 km = 1000m
1 mile = 1.6 kms = 1600 mts
1 hr = 60 minutes = 3600 seconds
1 km/hr = 1000m/hour = 1000m/3600 seconds or 5/18 m/s
1m/s = (1/1000) km/ (1/3600) hours = 18/5 km/hr
To convert km/hr to m/s, multiply by 5/18
To convert from m/s to km/hr, multiply by 18/5
Time
Distance

3. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
3
Travelling at of his usual speed, Arvind reaches the restaurant 10
minutes early. How long did he take to reach the restaurant this time?
Q.
th
8
9

4. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
4
Travelling at of his usual speed, Arvind reaches the restaurant 10
minutes early. How long did he take to reach the restaurant this time?
of usual speed implies that it takes of usual time for Arvind to
reach the restaurant.
He saves of usual time. This corresponds to 10 mins.
Thus, the usual timing = 9 * 10 = 90 mins
Since he reached 10 mins earlier 90 - 10 = 80 mins is the time taken by
Arvind to reach the restaurant today.
A.
th
8
9
th
9
8
th
8
9
th
9
1

5. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
5
Cycling at a speed of 10 km/h from his residence, Rajesh reached the
railway station 3 minutes late. Had he cycled at a speed of 12 km/h he
would have reached 3 minutes early. What is the distance between his
house and the railway station?
Q.

6. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
6
Cycling at a speed of 10 km/h from his residence, Rajesh reached the
railway station 3 minutes late. Had he cycled at a speed of 12 km/h he
would have reached 3 minutes early. What is the distance between his
house and the railway station?
Distance covered in both cases is the same
Speed Time
10 kmph t + hrs
12 kmph t - hrs
A.
60
3
60
3

7. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
7
So we equate them.
10 * (t + ) = 12 * ( t - )
2t =
t =
Distance = 12 * = 6 km
Therefore, The distance between his house and the railway station is 6
km.
60
3
60
3
10
11
10
56
2
1
5
3
=
+
=+
20
11
60
360
60
3
20
11
=





−

8. 2IIM
Ascent Education’s
An IIM Alumni Venture
Theory
Speed Time Distance – Some prototypes
8
 A travels from point X to Y a distance of 100 km, B who starts at the same
time as A starts from point Y and moves towards X. If A and B travel at a
km/hr and b km/hr respectively, after how long will they meet?
 When they meet, both should have travelled the same amount of
time. Or =
 Travelling at 8/7 th of his usual speed, Arvind reaches the restaurant 10
minutes early. How long did he take to reach the restaurant this time
 The distance travelled in both cases is the same. So, if Arvind travels
at of his usual speed, he will take of his usual time
a
x
b
x-100
th
7
8 th
8
7

9. 2IIM
Ascent Education’s
An IIM Alumni Venture
Theory
Speed Time Distance – Average speed and relative speed
9
 Average Speed =
 Relative speed is the speed at which one object is approaching or
receding from another.
 When A and B travel in the same direction, relative speed = Sa - Sb
 When A and B travel in opposite directions, relative speed = Sa + Sb
 All the formulae that we use in the normal context can be extended to
relative speeds also.
 Relative speed =
 Relative Distance = Relative Speed * Time
TimeTotal
DistanceTotal
Time
DistanceRelative

10. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
10
Anand travels the first 30 minutes of the journey at a speed of 80 kmph
and the balance 90 minutes of his journey at a speed of 40 kmph. What
is the average speed of his journey in kmph?
Q.

11. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
11
Anand travels the first 30 minutes of the journey at a speed of 80 kmph
and the balance 90 minutes of his journey at a speed of 40 kmph. What
is the average speed of his journey in kmph?
Distance travelled during the first 30 minutes = 80 * = 40 km. ( since
the speed is in kmph we are converting the 30 minutes to hour)
Distance covered during the next 90 minutes = 40 * = 60 km.
Total Distance travelled = 40 + 60 = 100 km
Time taken = 2 hours
Average speed = 100/2 = 50 km/hr
A.
60
30
60
90

12. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
12
A car covers a third of the distance between two cities at a speed of 30
kmph and the balance distance at a speed of 60 kmph. What is the
average speed of the car?
Q.

13. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
13
A car covers a third of the distance between two cities at a speed of 30
kmph and the balance distance at a speed of 60 kmph. What is the
average speed of the car?
Let us assume the overall distance = 90 km. The car travels the first 30km
at 30 kmph and the remaining 60 km at 60 kmph.
Total time taken = 30/30 + 60/60 = 2 hours.
Average speed = 90/2 = 45kmph
A.

14. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
14
Ram leaves Bangalore at 4 PM in his car and travels to Chennai at 50
kmph. Shyam leaves Chennai at 5 PM and travels in his bike at 60 kmph
to Bangalore along the same route. If the distance between Bangalore
and Chennai is 380 kms, when will Ram and Shyam meet and how far
from Bangalore will they meet?
Q.

15. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
15
Ram leaves Bangalore at 4 PM in his car and travels to Chennai at 50
kmph. Shyam leaves Chennai at 5 PM and travels in his bike at 60 kmph
to Bangalore along the same route. If the distance between Bangalore
and Chennai is 380 kms, when will Ram and Shyam meet and how far
from Bangalore will they meet?
The relative speed between them = 50 + 60 = 110 kmph
When Shyam started, distance travelled by Ram = 1 * 50 = 50 km.
The distance between the two at 5 PM = 380 - 50 = 300 km.
Time at which they meet = = 3 hours
3 hours from 5 PM is 8 PM
A.
110
330

16. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
16
So in total Shyam travels 3 hours when they meet.
Distance travelled by Shyam in 3 hours = 3 * 60 = 180 km. So they meet
at a point 200km from Bangalore.

17. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
17
A train travelling at a speed of 72 mph crosses a platform of length 1400
meters completely in 60 seconds. What is the length of the train in
meters. Use conversion: 1 mile = 1600 meters
Q.

18. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
18
A train travelling at a speed of 72 mph crosses a platform of length 1400
meters completely in 60 seconds. What is the length of the train in
meters. Use conversion: 1 mile = 1600 meters
Distance travelled by the train = length of the train + length of the
platform.
Distance covered by train in 60 sec = 72* * 1.6 * 60 ( is the
conversion of speed from mph to meters per second)
= 1920 m.
Length of the train = 1920 - length of the platform
= 1920 - 1400
= 520 m
A.
18
5
18
5

19. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
19
A passenger train traveling at 70 kmph crosses a freight train, of length
400 m traveling in the opposite direction at a speed of 38 kmph,
completely in 25 seconds. What is the length of the passenger train in
meters?
Q.

20. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
20
A passenger train traveling at 70 kmph crosses a freight train, of length
400 m traveling in the opposite direction at a speed of 38 kmph,
completely in 25 seconds. What is the length of the passenger train in
meters?
Relative speed = 70 + 38 = 108 kmph
Distance covered = 25 * 108 * = 750 meters
But, Distance covered = length of train A + length of train B
750 = 400 + length of passenger train
Therefore length of passenger train = 750 - 400 = 350 m
A.
18
5

21. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
21
A boat travels from city A to city B, a distance of 72 km. The onward
journey is a downstream journey and the return journey is an upstream
one. If the round trip took the boat 7 hours and the speed of the stream
is 3 kmph, what was its speed in the return journey?
Q.

22. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
22
A boat travels from city A to city B, a distance of 72 km. The onward
journey is a downstream journey and the return journey is an upstream
one. If the round trip took the boat 7 hours and the speed of the stream
is 3 kmph, what was its speed in the return journey?
Let ‘x’ be the speed of the boat in Still water.
Now , the total distance covered = 144 km
Upstream speed = x - 3
Downstream speed = x + 3
Time taken to travel 72 km upstream =
Time taken to travel 72 km downstream =
Total time = 7 hours
A.
3x
72
−
3x
72
+

23. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
23
= 7
= 7
72x - 216 + 72x + 216 = 7x2
- 63
7x2
- 144x - 63 = 0
The solutions are x = 21 or x = - 3, speed can’t be negative.
Thus, x = 21
And the upstream speed = x - 3 = 21 - 3 = 18 kmph
Speed of the boat during the return journey = 18 kmph
3x
72
3x
72
−
+
+
9x
3)72(x3)72(x
2
−
++−