Speed, Time and Distance


  1. A train overtakes two person walking at 2 km per hr. and 4 km per hr. respectively and
    passes completely them in 9 sec. and 10 sec. respectively. What is the length of the train?









  1. View Hint View Answer Discuss in Forum

    Let the length of the train be x km and its speed y km per hr.
    Case I : When it passes the man walking at 2 km per hr. in the same direction
    Relative speed of train = (y – 2) km per hr.

    ∴  
    x
    = 9 seconds
    y − 2

    =
    9
    =
    1
    hour    ...(i)
    3600400

    Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
    Relative speed of train= (y – 4) km per hr.
    ∴  
    x
    = 10 sec.
    y − 4

    ⇒ 
    x
    =
    10
    hrs.
    y − 43600

    ⇒ 
    x
    =
    1
    hrs.    ...(ii)
    y − 4360

    On dividing equation (i) by (ii),
    we have
    y − 4
    =
    1/400
    =
    360
    =
    9
    y − 21/36040010

    ⇒  10y – 40 = 9y – 18
    ⇒  10y – 9y = 40 – 18
    ⇒  y = 22 km per hr.
    ∴  From equaton (i), we have
    ⇒ 
    x
    =
    1
    22 − 2400

    ⇒ x =
    1
    km
    20

    =
    1000
    = 50 metres.
    20

    Correct Option: D

    Let the length of the train be x km and its speed y km per hr.
    Case I : When it passes the man walking at 2 km per hr. in the same direction
    Relative speed of train = (y – 2) km per hr.

    ∴  
    x
    = 9 seconds
    y − 2

    =
    9
    =
    1
    hour    ...(i)
    3600400

    Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
    Relative speed of train= (y – 4) km per hr.
    ∴  
    x
    = 10 sec.
    y − 4

    ⇒ 
    x
    =
    10
    hrs.
    y − 43600

    ⇒ 
    x
    =
    1
    hrs.    ...(ii)
    y − 4360

    On dividing equation (i) by (ii),
    we have
    y − 4
    =
    1/400
    =
    360
    =
    9
    y − 21/36040010

    ⇒  10y – 40 = 9y – 18
    ⇒  10y – 9y = 40 – 18
    ⇒  y = 22 km per hr.
    ∴  From equaton (i), we have
    ⇒ 
    x
    =
    1
    22 − 2400

    ⇒ x =
    1
    km
    20

    =
    1000
    = 50 metres.
    20


  1. A train travelling at the rate of 60 km per hr, while inside a tunnel, meets another train of half its length travelling at 90 km per hr.
    and passes completely in 4
    1
    seconds.
    2
    Find the length of the tunnel if the first train passes completely
    through it in 4 minutes 37
    1
    seconds.
    2









  1. View Hint View Answer Discuss in Forum

    Trains are running in opposite direction.
    ∴  Relative speed of the two trains
    = 90 + 60 = 150 km per hr.

    Distance travelled in 4
    1
    seconds
    2

    with speed of 150 km per hr.
    = 150 ×
    5
    m per sec.
    18

    = 150 ×
    5
    ×
    9
    182

    =
    375
    metres
    2

    Let the length of the first train be x metres.
    Then the length of the second train be
    x
    metres
    2

    ∴   x +
    x
    =
    375
    22

    ⇒ 
    3x
    =
    375
    22

    ⇒  3x = 375
    ⇒  x = 125 metres
    Hence, the length of the first
    train = 125 metres
    Speed of the first train = 60 km per hr.
    = 60 ×
    5
    m per sec.
    18

    =
    50
    m per sec.
    3

    Time taken by the first train to cross the tunnel = 4 minutes
    and 37
    1
    sec.
    2

    = 240 +
    75
    sec. =
    480 + 75
    22

    =
    555
    sec.
    2

    Speed of first train =
    50
    m per sec.
    3

    ∴  Distance covered by it in
    555
    sec.
    2

    =
    50
    ×
    555
    = 4625 metres
    32

    Hence, length of tunnel
    = 4625 – 125 = 4500 metres
    = 4.5 km

    Correct Option: C

    Trains are running in opposite direction.
    ∴  Relative speed of the two trains
    = 90 + 60 = 150 km per hr.

    Distance travelled in 4
    1
    seconds
    2

    with speed of 150 km per hr.
    = 150 ×
    5
    m per sec.
    18

    = 150 ×
    5
    ×
    9
    182

    =
    375
    metres
    2

    Let the length of the first train be x metres.
    Then the length of the second train be
    x
    metres
    2

    ∴   x +
    x
    =
    375
    22

    ⇒ 
    3x
    =
    375
    22

    ⇒  3x = 375
    ⇒  x = 125 metres
    Hence, the length of the first
    train = 125 metres
    Speed of the first train = 60 km per hr.
    = 60 ×
    5
    m per sec.
    18

    =
    50
    m per sec.
    3

    Time taken by the first train to cross the tunnel = 4 minutes
    and 37
    1
    sec.
    2

    = 240 +
    75
    sec. =
    480 + 75
    22

    =
    555
    sec.
    2

    Speed of first train =
    50
    m per sec.
    3

    ∴  Distance covered by it in
    555
    sec.
    2

    =
    50
    ×
    555
    = 4625 metres
    32

    Hence, length of tunnel
    = 4625 – 125 = 4500 metres
    = 4.5 km



  1. Two trains 200 metres and 175 metres long are running on parallel lines.
    They take 7
    1
    seconds.when running in opposite directions
    2
    and 37
    1
    seconds when running in the same direction
    2
    to pass each other. Find their speeds in km per hour.









  1. View Hint View Answer Discuss in Forum

    Let the speed of the train be x metre per sec. and y metre per sec. respectively.
    Sum of the length of the trains = 200 + 175 = 375 metres
    Case : I
    When the trains are moving in opposite directions
    Relative speed = (x + y) m per sec.
    In this case the time taken by the trains to cross each other

    =
    375
    sec.
    x + y

    ∴ 
    375
    =
    15
    x + y2

    ⇒  x + y = 50     ...(i)
    Case : II
    When the trains are moving in the same direction.
    Relative speed = (x – y) m per sec.
    In this case, the time taken by the trains to cross each other
    =
    375
    sec.
    x − y

    ∴ 
    375
    =
    75
    x − y2

    ⇒  x – y = 10     ...(ii)
    Now, x + y = 50
    x – y = 10
    _________
    2x = 60

    ⇒  x = 30
    Putting this value in equation (i),
    we have
    y = 50 – 30 = 20
    ∴  Speed of trains = 30 m per sec.
    = 30 ×
    18
    = 108 km per hr.
    5

    and 20 m per sec. = 20 ×
    18
    = 72 km per hr.
    5

    Correct Option: B

    Let the speed of the train be x metre per sec. and y metre per sec. respectively.
    Sum of the length of the trains = 200 + 175 = 375 metres
    Case : I
    When the trains are moving in opposite directions
    Relative speed = (x + y) m per sec.
    In this case the time taken by the trains to cross each other

    =
    375
    sec.
    x + y

    ∴ 
    375
    =
    15
    x + y2

    ⇒  x + y = 50     ...(i)
    Case : II
    When the trains are moving in the same direction.
    Relative speed = (x – y) m per sec.
    In this case, the time taken by the trains to cross each other
    =
    375
    sec.
    x − y

    ∴ 
    375
    =
    75
    x − y2

    ⇒  x – y = 10     ...(ii)
    Now, x + y = 50
    x – y = 10
    _________
    2x = 60

    ⇒  x = 30
    Putting this value in equation (i),
    we have
    y = 50 – 30 = 20
    ∴  Speed of trains = 30 m per sec.
    = 30 ×
    18
    = 108 km per hr.
    5

    and 20 m per sec. = 20 ×
    18
    = 72 km per hr.
    5


  1. A train running at 25 km per hour take 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at the rate of 5 km per hr. in the same direction. Find the length of the platform.









  1. View Hint View Answer Discuss in Forum

    Let the length of train be x metres and the length of platform be y metres.

    Speed of the train = 25 ×
    5
    m/sec
    18

    =
    125
    m per sec.
    18

    Time taken by train to pass the platform
    = (x + y) ×
    18
    sec.
    125

    ∴  (x + y) ×
    18
    = 18
    125

    or,  x + y = 125    ...(i)
    Speed of train relative to man = (25 + 5) km per hr.
    = 30 ×
    5
    m per sec.
    18

    =
    25
    m per sec.
    3

    Time taken by the train to pass the man
    = x ×
    3
    sec.
    25

    =
    3x
    sec.
    25

    ∴ 
    3x
    = 12
    25

    ⇒  x =
    25 × 12
    = 100 metres
    3

    Putting x = 100 in equation (i),
    we get, y = 25 metres.
    ∴  Length of train = 100 metres
    and length of the platform = 25 metres.

    Correct Option: A

    Let the length of train be x metres and the length of platform be y metres.

    Speed of the train = 25 ×
    5
    m/sec
    18

    =
    125
    m per sec.
    18

    Time taken by train to pass the platform
    = (x + y) ×
    18
    sec.
    125

    ∴  (x + y) ×
    18
    = 18
    125

    or,  x + y = 125    ...(i)
    Speed of train relative to man = (25 + 5) km per hr.
    = 30 ×
    5
    m per sec.
    18

    =
    25
    m per sec.
    3

    Time taken by the train to pass the man
    = x ×
    3
    sec.
    25

    =
    3x
    sec.
    25

    ∴ 
    3x
    = 12
    25

    ⇒  x =
    25 × 12
    = 100 metres
    3

    Putting x = 100 in equation (i),
    we get, y = 25 metres.
    ∴  Length of train = 100 metres
    and length of the platform = 25 metres.



  1. Two places A and B are 162 kms apart. A train leaves A for B and at the same time another train leaves B for A. The two trains meet at the end of 6 hours. If the train travelling from A to B travels 8 km per hr. faster than the other, find the speed of the faster train.









  1. View Hint View Answer Discuss in Forum

    Both trains meet after 6 hours.
    ∴  The relative speed of two trains

    =
    162
    = 27 km per hr.
    6

    The speed of the slower train starting from B
    =
    27 − 8
    =
    19
    =9
    1
    km per hr.
    222

    ∴  The speed of the faster train
    = 9
    1
    + 8 = 17
    1
    km per hr.
    22

    Correct Option: D

    Both trains meet after 6 hours.
    ∴  The relative speed of two trains

    =
    162
    = 27 km per hr.
    6

    The speed of the slower train starting from B
    =
    27 − 8
    =
    19
    =9
    1
    km per hr.
    222

    ∴  The speed of the faster train
    = 9
    1
    + 8 = 17
    1
    km per hr.
    22