Speed, Time and Distance


  1. Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction ?
    1. 16
    2. 15
    3. 12
    4. 10

  1. View Hint View Answer Discuss in Forum

    When a train crosses a telegraph post, it covers its own length.

    ∴  Speed of first train =
    120
    = 12 m/sec.
    10

    Speed of second train =
    120
    = 8 m/sec.
    15

    Relative speed = 12 + 8 = 20 m/sec.
    Required time =
    Total length of trains
    Relative Speed

    =
    2 × 120
    = 12 seconds.
    20

    Correct Option: C

    When a train crosses a telegraph post, it covers its own length.

    ∴  Speed of first train =
    120
    = 12 m/sec.
    10

    Speed of second train =
    120
    = 8 m/sec.
    15

    Relative speed = 12 + 8 = 20 m/sec.
    Required time =
    Total length of trains
    Relative Speed

    =
    2 × 120
    = 12 seconds.
    20


  1. Two trains of length 70 m and 80 m are running at speed of 68 km/hr and 40 km/hr respectively on parallel tracks in opposite directions. In how many seconds will they pass each other ?
    1. 10 sec
    2. 8 sec
    3. 5 sec
    4. 3 sec

  1. View Hint View Answer Discuss in Forum

    Relative speed
    = (68 + 40) kmph = 108 kmph

    =
    108 × 5
    m/s or 30 m/s
    18

    ∴  Required time =
    Sum of the lengths of both trains
    Relative Speed

    =
    70 + 80
    second = 5 seconds
    30

    Correct Option: C

    Relative speed
    = (68 + 40) kmph = 108 kmph

    =
    108 × 5
    m/s or 30 m/s
    18

    ∴  Required time =
    Sum of the lengths of both trains
    Relative Speed

    =
    70 + 80
    second = 5 seconds
    30



  1. Two towns A and B are 500 km. apart. A train starts at 8 AM from A towards B at a speed of 70 km/hr. At 10 AM, another train starts from B towards A at a speed of 110 km/hr. When will the two trains meet ?
    1. 1 PM
    2. 12 Noon
    3. 12.30 PM
    4. 1.30 PM

  1. View Hint View Answer Discuss in Forum

    Let two trains meet after t hours when the train from town A leaves at 8 AM.
    ∴  Distance covered in t hours at 70 kmph + Distance covered in
    (t – 2) hours at 110 kmph = 500km
    ∴  70t + 110 (t – 2) = 500
    ⇒  70t + 110t – 220 = 500
    ⇒  180 t = 500 + 220 = 720

    ⇒  t =
    720
    = 4 hours
    180

    Hence, the trains will meet at 12 noon.

    Correct Option: B

    Let two trains meet after t hours when the train from town A leaves at 8 AM.
    ∴  Distance covered in t hours at 70 kmph + Distance covered in
    (t – 2) hours at 110 kmph = 500km
    ∴  70t + 110 (t – 2) = 500
    ⇒  70t + 110t – 220 = 500
    ⇒  180 t = 500 + 220 = 720

    ⇒  t =
    720
    = 4 hours
    180

    Hence, the trains will meet at 12 noon.


  1. A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the railway platform is
    1. 200 m
    2. 300 m
    3. 350 m
    4. 400 m

  1. View Hint View Answer Discuss in Forum

    Let the length of the train travelling at 48 kmph be x metres.
    Let the length of the platform be y metres.
    Relative speed of train
    = (48 + 42) kmph

    =
    90 × 5
    m./sec.
    18

    = 25 m./sec.
    and 48 kmph
    =
    48 × 5
    =
    40
    m./sec.
    183

    According to the question,
    x +
    1
    = 2
    25

    = 12
    ⇒ 
    3x
    = 12
    2 × 25

    ⇒  3x = 2 × 12 × 25 = 600
    ⇒  x = 200 m.
    Also, 
    200 + y
    = 45
    40/3

    ⇒  600 + 3y = 40 × 45
    ⇒  3y = 1800 – 600 = 1200
    ⇒  y =
    1200
    = 400 m.
    3

    Correct Option: D

    Let the length of the train travelling at 48 kmph be x metres.
    Let the length of the platform be y metres.
    Relative speed of train
    = (48 + 42) kmph

    =
    90 × 5
    m./sec.
    18

    = 25 m./sec.
    and 48 kmph
    =
    48 × 5
    =
    40
    m./sec.
    183

    According to the question,
    x +
    1
    = 2
    25

    = 12
    ⇒ 
    3x
    = 12
    2 × 25

    ⇒  3x = 2 × 12 × 25 = 600
    ⇒  x = 200 m.
    Also, 
    200 + y
    = 45
    40/3

    ⇒  600 + 3y = 40 × 45
    ⇒  3y = 1800 – 600 = 1200
    ⇒  y =
    1200
    = 400 m.
    3



  1. A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train is
    1. 45 km./hr
    2. 48 km./hr
    3. 52 km./hr
    4. 54 km./hr

  1. View Hint View Answer Discuss in Forum

    Let the speed of the second train be x m/s

    Speed of first train =
    150
    = 10 m/sec
    15

    Relative speed of trains
    = (x + 10) m/s
    Total distance covered
    = 150 + 150 = 300 metre
    ∴  Time taken =
    300
    x + 10

    ⇒ 
    300
    = 12
    x + 10

    ⇒  12x + 120 = 300
    ⇒  12x = 300 – 120 = 180
    ⇒  x =
    180
    = 15 m/s
    12

    =
    15 × 18
    or 54 kmph.
    5

    Correct Option: D

    Let the speed of the second train be x m/s

    Speed of first train =
    150
    = 10 m/sec
    15

    Relative speed of trains
    = (x + 10) m/s
    Total distance covered
    = 150 + 150 = 300 metre
    ∴  Time taken =
    300
    x + 10

    ⇒ 
    300
    = 12
    x + 10

    ⇒  12x + 120 = 300
    ⇒  12x = 300 – 120 = 180
    ⇒  x =
    180
    = 15 m/s
    12

    =
    15 × 18
    or 54 kmph.
    5