TSD.pptx

QUANTITATIVE ABILITY SESSION
TIME, SPEED & DISTANCE
By: ANKUR AGARWAL
MENTOR & EDUCATOR

Speed, Time & Distance is one of the most
common quantitative aptitude topics asked in
exams. This is one of those topics which
candidates are familiar with even before they
start their competitive exam preparation.
The concept of Speed, Time, Distance remains
the same, however, the type of questions asked
in the examinations may have a different variety.
The concept of Speed, Time and Distance is
used extensively for questions relating to different
topics such as motion in a straight line, circular
motion, boats and streams, races, clocks, etc.
TIME, SPEED & DISTANCE - Introduction & Concept

Relationship Between TIME, SPEED & DISTANCE
Speed = Distance / Time – This tells us how
slow or fast an object moves. It describes the
distance travelled divided by the time taken to
cover the distance.
Distance = Speed X Time - Speed is directly
Proportional to Distance and Inversely
proportional to Time.
Time = Distance / Speed - as the speed
increases the time taken will decrease and vice
versa.

Relationship Between TIME, SPEED & DISTANCE
If two bodies move at the same speed, the
distances covered by them are directly
proportionality to the times of travel. i.e. when s is
constant.
If two bodies move for the same time period, the
distances covered by them are directly
proportional to the speeds of travel. i.e. when t is
constant.
If two bodies move for the same distance, their
times of travel are inversely proportional to the
speeds of travel. i.e. when d is constant.

Units of TIME, SPEED & DISTANCE
Each Speed, Distance and Time can be
expressed in different units:
Time: seconds(s), minutes (min), hours (hr)
Distance: meters (m), kilometers (km), miles, feet
Speed: m/s, km/hr

TIME, SPEED & DISTANCE Conversions
1 km / hour = 5 / 18 m / sec
1 m / sec = 18 / 5 km / hour = 3.6 km / hour
1 km/hr = 5/8 miles/hour
1 yard = 3 feet
1 kilometer= 1000 meters = 0.6214 mile
1 mile= 1.609 kilometer
1 hour= 60 minutes= 60*60 seconds= 3600 seconds
1 mile = 1760 yards
1 yard = 3 feet
1 mile = 5280 feet
1 mph = (1 x 1760) / (1 x 3600) = 22/45 yards/sec
1 mph = (1 x 5280) / (1 x 3600) = 22/15 ft/sec

Key Rule for Ratio based Problems of TIME, SPEED & DISTANCE
If two objects have their speeds in the ratio a:b,
distance covered by the two objects in the same
time will be in the ratio a:b and time taken by the
two objects to cover same distance will be in the
ratio b:a.
The ratio concept can be applied only when one
of the given distance, time or speed is constant.

PROPORTIONALITY IN TIME, SPEED & DISTANCE
Distance Same => Speed (S) x Time (T) = Constant => S1T1 = S2T2
If S1 : S2 = a :b then T1: T2 = b : a ------- Inversely Proportional
If I change my speed 4/5 of the normal speed, then I reach 15 minutes late to
my office. What is the normal time taken by me from home to office?

Speed Same => Distance (D) / Time (T) = Constant => D1 / D2 = T1 / T2
If D1 : D2 = a :b then T1 : T2 =a : b ------- Directly Proportional

Time Same => Distance (D) / Speed (S) = Constant => D1 / D2 = S1 / S2
If D1 : D2 = a :b then S 1 : S2 = a : b ------- Directly Proportional

A train covers 50 km and meets with an accident & moves at 4/5 of its original
speed & reaches its destination 45 minutes late. Had the accident occur 20 km
further on, the train would have arrived 12 min sooner. Find –
1. Normal Speed
2. Normal Time
3. Distance between source & destination

TIME, SPEED & DISTANCE - Average Speed
Average Speed = (Total distance traveled) / (Total time taken)
Case 1 – When the distance is
constant: Average speed = 2xy / x+y; Where, x
and y are the two speeds at which the same
distance has been covered.
Case 2 – When the time taken is
constant: Average speed = (x + y) / 2; Where,
x and y are the two speeds at which we traveled
for the same time.

A car travels one-third of the distance on a straight road at 10 km/h, the next
one-third at 20 km/h and the remaining at 60 km/h. What is the average speed
of the car for the whole journey?

TIME, SPEED & DISTANCE – RELATIVE SPEED
“Relative” means “in comparison to”. Thus, the
relative speed is used when two or more bodies
moving with some speed are considered.
To make things simpler, one body can be made
stationary (i.e. Speed =zero) and take the speed of
the other body with respect to the stationary body,
which is the sum of the speed if the bodies are
moving in the opposite direction and the difference if
they are moving in the same direction.
This speed of the moving body with respect to the
stationary body is called the relative Speed.

If two bodies are moving at different speeds in the same direction, then their
relative speed can be determined by the difference between their speeds. It can
be expressed by -
Relative speed when bodies move in the same
direction is given by – ( V1 - V2 )

If two bodies are moving at different speeds in the opposite direction, then their
relative speed can be determined by the summation of their speeds. It can be
expressed by -
Relative speed when bodies move in the opposite
direction is given by – ( V1 + V2 )

Difficulties of Determining TIME, SPEED & DISTANCE – RELATIVE SPEED
Meeting Time and Travel Time: If two moving body has
started to moves towards each other at the same time
maintaining the same speed, calculating their meeting
point can be tricky. Though the distances covered by
them should remain proportional to their speed.
Issues Related to the Ratio: When two moving bodies
are following the same path, determining Relative
Speeds may lead to some ration-based errors. For
example- X body and Y body are moving in the same
direction with the similar speed and the speed and
distance is mentioned as X:Y. But it can also be Y:X as
per the time to cover the same distance. But in this case
the distance, speed and time must remain constant.

Difficulties of Determining TIME, SPEED & DISTANCE – RELATIVE SPEED
Traveling By Boat: In this type of calculation the speed
of the river flow must be taken into consideration. But the
speed of the river flowing can not be counted as a
constant. For example, a boat can travel a certain
distance but the situations like up-streams and down-
streams will affect the calculation.

TIME, SPEED & DISTANCE – RELATIVE SPEED FORMUA
Let the speed of the first body be: x km/hr.
And the speed of the second body is y km/hr.
So, their relative speed is equal to (x – y) km/hr x>y
Then,
The time after which both bodies meet
= distance traveled / relative speed
= d km / (x – y) km/hr
If two bodies moving at a different speed in the SAME direction.

TIME, SPEED & DISTANCE – RELATIVE SPEED FORMUA
Let the speed of the first body be: x km/hr.
And the speed of the second body is y km/hr.
So, their relative speed is equal to (x + y) km/hr
Then,
The time after which both bodies meet
= distance traveled / relative speed
= d km / (x + y) km/hr
If two bodies moving at a different speed in the OPPOSITE direction.

TIME, SPEED & DISTANCE – RELATIVE SPEED OBJECT CROSSING
Time taken for two objects to cross, T = Total length of objects / Relative Speed

TIME, SPEED & DISTANCE – RACES
A race is a competition of speed in which contestants compete among
themselves to cover some distance in shortest length of time.
Linear race: In this case participate compete in
linear race track.
Circular race: In this case the path of the race is
circular in shape.
Starting point: It’s the point from where the race
begins.
Winning Point: It’s the end point of the race.

TIME, SPEED & DISTANCE – LINEAR RACES
Expression Meaning
Head-Start / A gives
B start of x meters
When a racer gets a start x meters ahead of
the starting point it’s called head-start of x
meters. Here A gives B a head-start of x
meters.
Head-Start/ A can
give B a start of t
minutes
When a contestant gets a start by t seconds
earlier than other ones, it’s called head-start of
t seconds. Here A gives B a head-start of t
seconds.
A beats B by x
meters
When A reaches the winning point before B
and is x meters away from B. Then A beats B
by x meters.
A beats B by t
seconds
When A reaches the winning point t seconds
before B. Then A beats B by t meters.
Dead Heat
A dead heat is a situation of tie. When all the
participants reach the winning point at the
same point.

In a race of 100m, A beats B by 20m & beats C b 30m. Then in other race of
100m, by how many meters will B beat C?

In a race of 100m, A beats B by 20m. In other race of 100m, B beats C by 30m.
Then in other race of 100m, by how many meters will A beat C?

In a race of 100m, A beats B either by 20m or 5 sec. Find the speed of A.

TIME, SPEED & DISTANCE – CIRCULAR RACES
The questions asked in this concept are usually of following types:
When do the participants meet first anywhere on the track?
How many times do the participants meet?
When do the first time they meet at the starting point or ending point?

TIME, SPEED & DISTANCE – CIRCULAR RACES TIPS
Let X and Y be two runners running in circular path of length L with speeds x
m/s and y m/s respectively. If x > y then,
X and Y are running in the SAME direction then time taken by
X and Y to meet first
time anywhere on the
track
time at the starting
point on the track
L/ (x – y) LCM of L/x and L/y

Let X and Y be two runners running in circular path of length L with speeds x
m/s and y m/s respectively. If x > y then,
X and Y are running in the OPPOSITE direction then time taken by
time anywhere on the
track
time at the starting
point on the track
L/ (x + y) LCM of L/x and L/y

When the speed of Y is expressed in terms of X
and X and Y are running in opposite direction
such that speed of Y is n times of X then no. of
meeting points of X and Y are n + 1 i.e. if speed
of Y is equal to X then their meeting points are 2.
If the no. of meeting points is known and the time
required to meet at the starting point is also
known then you can compute the time needed
for them to meet for the first time using the
formula.

Time after which they’ll meet at the starting point) / no. of meeting points
X and Y running in circular track and in opposite
direction. If the speed of X is x/y of Y, then the total
number of meeting points = x + y.
All the distant meeting points are equidistant in
circular path and same goes for time i.e. all of them
take equal time and are covered in definite
manner.
A diagrammatic approach is the best technique
when it comes to circular path. It will help you
visualize the question properly.

Number of distinct meeting points on a circular track
1. Find the ratio of their speed in its simplest form (say a:b)
2. If both are moving in the same direction, then find the absolute difference
between a and b, i.e., |a-b|.
This absolute difference will be the number of distinct
meeting points on the circular track. Also, observed:
All the meeting points are uniformly distributed on the
track.
The starting point will always be one of the meeting
points and it is also the last meeting point.
If the difference between a and b is ODD, then they will
never meet at-the diametrically opposite point.

TIME, SPEED & DISTANCE – BOATS & STREAMS CONCEPTS
This topic basically deals with calculating the speed of anything in the water
when it flows along with the flow of water or in the opposite direction.
Stream – The moving water in a river is called a
stream.
Upstream – If the boat is flowing in the opposite
direction to the stream, it is called upstream.
Downstream – If the boat is flowing along the
direction of the stream, it is called downstream.
Still Water – Under any circumstance the water is
considered to be stationary and the speed of the
water is zero.

TIME, SPEED & DISTANCE – Commonly Asked Question in
BOATS & STREAMS
Time Related Questions: The speed of the stream
and the speed of the boat in still water will be given and
the question will be to find the time taken by a boat to
go downstream or upstream or both.
Speed Related Questions: The speed of a boat
upstream and downstream will be given and you will be
asked to find the speed of the boat in still water or the
speed of the stream.
Average Speed Questions: The average speed of the
boat can be asked. The speed of the boat upstream
and downstream will be provided in the question.
Distance Related Questions: The distance traveled
will be asked. The time taken by the boat to reach a
point upstream and downstream will be given.

TIME, SPEED & DISTANCE – BOATS & STREAMS FORMULA
Speed of Boat in Still Water = ½ (Downstream
Speed + Upstream Speed)
Speed of Stream = ½ (Downstream Speed –
Upstream Speed)
Average Speed of Boat = {(Upstream Speed ×
Downstream Speed) / Boat’s Speed in Still Water}
“u” = the speed of the boat in still water
“v” = the speed of the stream
Upstream = (u−v) km/hr
Downstream = (u+v)Km/hr

TIME, SPEED & DISTANCE – Tips and Tricks to Solve BOATS &
STREAMS Questions
The first and most important tip is that a candidate
must memorize the important formulas to answer
the questions correctly. Memorizing the formulas
will help candidates answer straight forward
questions without making any errors.
Do not confuse yourselves between the concept
of upstream and downstream as the question may
not specifically mention the two terms and instead
mention “ in the direction of flow” or “against the
direction of flow”.

TIME, SPEED & DISTANCE – Tips and Tricks to Solve BOATS &
STREAMS Questions
Reading the questions carefully will help
candidates avoid making silly mistakes, so do not
be in a rush while reading the instructions
mentioned in the questions.
Ensure that you do not panic reading the length of
the question or the terms used in the questions as
boats and streams questions asked in the exams
are mostly direct and not too complex. It is just
the formation of the question that makes it sound
complicated.

TIME, SPEED & DISTANCE – BOATS & STREAMS
A boat whose speed in 20 km/hr in still water goes 40 km downstream and
comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:
1. 6 km/hr 2. 9 km/hr 3. 12 km/hr 4. 16 km/hr

A boat can travel 20 km downstream in 24 min. The ratio of the speed of the
boat in still water to the speed of the stream is 4 : 1. How much time will the
boat take to cover 15 km upstream?
1. 20 mins 2. 22 mins 3. 25 mins 4. 30 mins

A boat running upstream takes 9 hours 48 minutes to cover a certain distance,
while it takes 7 hours to cover the same distance running downstream. What is
the ratio between the speed of the boat and speed of the water current
respectively?
1. 5:2 2. 7:4 3. 6:1 4. 8:3

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