Speed, Time and Distance


  1. A train passes two persons walking in the same direction at a speed of 3 km/hour and 5km/hour respectively in 10 seconds and 11 seconds respectively. The speed of the train is
    1. 28 km/hour
    2. 27 km/hour
    3. 25 km/hour
    4. 24 km/hour

  1. View Hint View Answer Discuss in Forum

    Let the speed of train be x kmph and its length be y km.
    When the train crosses a man, it covers its own length
    According to he question,

    =
    y
    = 10
    (x − 3) ×
    5
    3

    ⇒  18 y = 10 × 5(x –3)
    ⇒  18y = 50x –150   ..... (i)
    and, 
    y
    = 11
    (x − 5) ×
    5
    18

    ⇒  18y = 55(x–5)
    ⇒  18y = 55x –275   .... (ii)
    From equations (i) and (ii),
    55x –275 = 50x–150
    ⇒  55x –50x = 275 – 150
    ⇒  5x = 125
    ⇒  x =
    125
    = 25
    5

    ∴  Speed of the train = 25 kmph
    Second Method :
    Here, S1 = 3, S2 = 5
    t1 =
    10
    ,  t2 =
    11
    36003600

    Speed of train =
    t1S1 − t2S2
    t1 − t2

    =
    3 × 10
    5 × 11
    36003600
    10
    11
    36003600

    =
    − 25
    ×
    3600
    3600− 1

    = 25 m/sec

    Correct Option: C

    Let the speed of train be x kmph and its length be y km.
    When the train crosses a man, it covers its own length
    According to he question,

    =
    y
    = 10
    (x − 3) ×
    5
    3

    ⇒  18 y = 10 × 5(x –3)
    ⇒  18y = 50x –150   ..... (i)
    and, 
    y
    = 11
    (x − 5) ×
    5
    18

    ⇒  18y = 55(x–5)
    ⇒  18y = 55x –275   .... (ii)
    From equations (i) and (ii),
    55x –275 = 50x–150
    ⇒  55x –50x = 275 – 150
    ⇒  5x = 125
    ⇒  x =
    125
    = 25
    5

    ∴  Speed of the train = 25 kmph
    Second Method :
    Here, S1 = 3, S2 = 5
    t1 =
    10
    ,  t2 =
    11
    36003600

    Speed of train =
    t1S1 − t2S2
    t1 − t2

    =
    3 × 10
    5 × 11
    36003600
    10
    11
    36003600

    =
    − 25
    ×
    3600
    3600− 1

    = 25 m/sec


  1. If a train, with a speed of 60 km/ hr, crosses a pole in 30 seconds, the length of the train (in metres) is :
    1. 1000
    2. 900
    3. 750
    4. 500

  1. View Hint View Answer Discuss in Forum

    Speed of train = 60 kmph

    = 60 ×
    5
    ×
    50
    m/sec
    183

    &there4:  Length of train
    = Speed × Time
    =
    50
    × 30 = 500 m
    3

    Correct Option: D

    Speed of train = 60 kmph

    = 60 ×
    5
    ×
    50
    m/sec
    183

    &there4:  Length of train
    = Speed × Time
    =
    50
    × 30 = 500 m
    3



  1. A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was
    1. 42
    2. 45
    3. 48
    4. 55

  1. View Hint View Answer Discuss in Forum

    Speed of train

    =
    120
    ×
    18
    = 48 kmph
    95

    Correct Option: C

    Speed of train

    =
    120
    ×
    18
    = 48 kmph
    95


  1. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hour ?
    1. 2.5 seconds
    2. 5 seconds
    3. 12.5 seconds
    4. 3
      5
      seconds
      4

  1. View Hint View Answer Discuss in Forum

    Speed of the train

    = 144 kmph = 144 ×
    5
    = 40 m/s
    18

    When a train crosses a pole, it covers a distance equal to its own length.
    The required time =
    100
    40

    =
    5
    = 2 5. seconds.
    2

    Correct Option: A

    Speed of the train

    = 144 kmph = 144 ×
    5
    = 40 m/s
    18

    When a train crosses a pole, it covers a distance equal to its own length.
    The required time =
    100
    40

    =
    5
    = 2 5. seconds.
    2



  1. A 75 metre long train is moving at 20 kmph. It will cross a man standing on the platform in
    1. 12 seconds
    2. 14 seconds
    3. 13.5 seconds
    4. 15.5 seconds

  1. View Hint View Answer Discuss in Forum

    Speed of train (in m/s) = 20 ×
    5
    =
    50
    m/sec
    189

    Required time =
    75
    × 9
    50

    = 13.5 seconds

    Correct Option: C

    Speed of train (in m/s) = 20 ×
    5
    =
    50
    m/sec
    189

    Required time =
    75
    × 9
    50

    = 13.5 seconds