Time and Distance Concept Class

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Time and Distance – Concept Class

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Basics of Time, Speed and Distance

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The relationship
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑆𝑝𝑒𝑒𝑑 ∗ 𝑡𝑖𝑚𝑒

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The relationship
Constant Time Speed Distance
Relationship
between the
other two
variables
D varies directly
with S
𝐷1
𝐷2
=
𝑆1
𝑆2
D varies directly
with T
𝐷1
𝐷2
=
𝑇1
𝑇2
T varies
Inversely with S
𝑇1
𝑇2
=
𝑆2
𝑆1

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Problems
Ashwin has to travel from one point to another point in a certain time.
Travelling at a speed of 6kmph he reaches 40m late and travelling at a speed
of 8kmph he reaches 12m earlier. What is the distance between this two
points ?
1) 27 km
2) 18 km
3) 5 km
4) 21 km
5) None of these Answer: option 5
SBI PO Prelims
(2016)

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Problems
If a train runs at 70 km/hour, it reaches its destination late by 12 minutes. But
if it runs at 80 km/hour, it is late by 3 minutes. The correct time to cover the
journey
1) 58 minutes
2) 2 hours
3) 1 hour
4) 59 minutes
Answer: option 3
SSC CGL
(2014)

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Average Speed

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Average speed
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑𝑓𝑜𝑟 2 𝑒𝑞𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑠 =
2𝑎𝑏
𝑎 + 𝑏

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Problems
A boy goes to school from his home at a speed of 4 km/hr and returns
at a speed of 6 km/hr. If in total he took 5 hours in going and coming
back, the distance between his house and school?
1) 8km
2) 10km
3) 12km
4) 14km
5) None of these
Answer: option 3
IBPS Clerks Pre
(2016)

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Problems
A car covers first 10 km with 40km/hr next 10km with 60 km and next 10 km
in 20 km/hr. What is the average speed of the car?
1) 320/11
2) 330/11
3) 350/11
4) 360/11
5) 355/11
Answer: option 4
IBPS Clerks Main
(2016)

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Relative Speed

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Relative speed
When in same direction,
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑆𝑝𝑒𝑒𝑑 𝑓𝑎𝑠𝑡𝑒𝑟 − 𝑆𝑝𝑒𝑒𝑑 𝑆𝑙𝑜𝑤𝑒𝑟
When in opposite direction,
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑆𝑝𝑒𝑒𝑑 𝑓𝑎𝑠𝑡𝑒𝑟 + 𝑆𝑝𝑒𝑒𝑑 𝑆𝑙𝑜𝑤𝑒𝑟

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Problems
A thief is noticed by a policeman from a distance of 200 m. The thief starts
running and the policeman chases him. The thief and the policeman run at
the rate of 10 km and 11 km per hour respectively. The distance (in metres)
between them after 6 minutes is
1) 190
2) 200
3) 100
4) 150
Answer: option 3
SSC CGL
(2012)

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Problems
The distance between two cities A and B is 330 km. A train starts from A at 8
a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m.
and travels towards A at 75 km/hr. At what time do they meet?
1) 10:30 am
2) 10:45 am
3) 11 am
4) 11:25 am
5) None of these
Answer: option 3
IBPS Clerks
(2015)

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Trains

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Trains – with a stationary object
A train and a stationary object
Stationary object – point object
𝑑 = 𝑙 𝑡𝑟𝑎𝑖𝑛
Problem: A train of length 300m crosses a pole in 1 minute.
What is the speed of the train?

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Problems
A train 180 mt long is running at a speed of 90 km/hr. How long will it take to
pass a post ?
1) 8.2 secs
2) 7.8 secs
3) 8 secs
4) 7.2 secs
Answer: option 4
SSC CGL
(2015)

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Trains – with a stationary object
A train and a stationary object
Stationary object – Platform
𝑑 = 𝑙 𝑡𝑟𝑎𝑖𝑛 + 𝑙 𝑝𝑙𝑎𝑡𝑓𝑜𝑟𝑚
Problem: A train of length 200 meters crosses a platform in
14 seconds. If the speed of the train is 25m/sec, what is the
length of the platform?

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Problems
A 360-metre-long train crosses a platform in 120 seconds. What is the speed
of the train?
1) 3 m/s
2) 5 m/s
3) 4.5 m/s
4) Cannot be determined
5) None of these
Answer: option 4
IBPS Clerks
(2011)

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Trains – with a moving object
A train and a moving object
Moving object – point object
• 𝑑 = 𝑙 𝑡𝑟𝑎𝑖𝑛
• 𝑆𝑝𝑒𝑒𝑑 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
Problem: A train of length 240 meters is travelling at a speed
of 35 m/sec. if the train takes 6 seconds to cross a cyclist who
is travelling towards the train. What is the speed of the
cyclist?

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Trains – with a moving object
A train and a moving object
Moving object – object with a defined length
• 𝑑 = 𝑙 𝑡𝑟𝑎𝑖𝑛 + 𝑙 𝑜𝑏𝑗𝑒𝑐𝑡
• 𝑆𝑝𝑒𝑒𝑑 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
Problem: A train of length 240 meters is travelling at a speed
of 35 m/sec. if the train takes 6 seconds to cross a cyclist who
is travelling towards the train. What is the speed of the
cyclist?

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Problems
A 210 m long train takes 6 s to cross a man running at 9 km/h in a direction
opposite to that of the train. What is the speed of the train? (in km/h)
1) 127
2) 121
3) 117
4) 108
5) 111
Answer: option 3
IBPS Clerks
(2013)

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Problems
Two trains of length 110 m and 90 m are running on parallel lines in the same
direction with a speed of 45km/h and 50 km/h respectively. In what time will
they pass other?
1) 136 s
2) 138 s
3) 142 s
4) 146 s
5) None of these
Answer: option 5 (144s)
IBPS SO
(2015)

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Boats and Streams

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Boats and Streams – Basic Terminology
Upstream
Downstream
Speed of Boat
Speed of the River

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Problems
A man rows 25 km downstream and 20 km upstream taking 5 h each time.
What is the velocity of the current?
1) 1 km/h
2) 2.5 km/h
3) 3.5 km/h
4) 4.5 km/h
5) None of these
Answer: option 5
(0.5km/hr)
IBPS SO
(2015)

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Problems
A boat running upstream takes 8 hours 48 minutes to cover a certain
distance, while it takes 4 hours to cover the same distance running
downstream. What is the ratio between the speed of the boat and speed of
water current respectively?
1) 2 : 1
2) 3 : 2
3) 8 : 3
4) Cannot be determined
5) None of these Answer: option 3
IBPS PO
(2014)

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Circular Tracks

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Circular Tracks
𝑑 = 𝐿𝑒𝑛𝑔𝑡ℎ 𝑇𝑟𝑎𝑐𝑘
𝑠 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑

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Problems
Harish, Dilip and Asha start running around a circular stadium and complete
one round in 27 seconds, 9 seconds and 36 seconds respectively. In how
much time will they meet again at the starting point?
1) 1 min 48 sec
2) 2 min 36 sec
3) 3 min 11 sec
4) 2 min 25 sec
5) None of these
Answer: option 1
IBPS Clerk
(2011)