Speed, Time and Distance


  1. Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?









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    Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
    kmph

    ⇒  20 ×
    10
    =
    8
    (20 + x )
    6060

    ⇒  200 = 160 + 8x
    ⇒  8x = 40
    ⇒  x =
    40
    = 5 kmph
    8

    Correct Option: C

    Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
    kmph

    ⇒  20 ×
    10
    =
    8
    (20 + x )
    6060

    ⇒  200 = 160 + 8x
    ⇒  8x = 40
    ⇒  x =
    40
    = 5 kmph
    8


  1. A passenger train 150m long is travelling with a speed of 36 km/ hr. If a man is cycling in the direction of train at 9 km/hr., the time taken by the train to pass the man is









  1. View Hint View Answer Discuss in Forum

    Relative speed of train
    = (36 – 9) kmph = 27 kmph

    =
    27 × 5
    m/sec
    18

    =
    15
    m/sec
    2

    ∴  Required time =
    Length of the train
    Relative speed

    =
    150 × 2
    = 20 seconds
    15

    Correct Option: D

    Relative speed of train
    = (36 – 9) kmph = 27 kmph

    =
    27 × 5
    m/sec
    18

    =
    15
    m/sec
    2

    ∴  Required time =
    Length of the train
    Relative speed

    =
    150 × 2
    = 20 seconds
    15



  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. 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. 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. 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