Speed, Time and Distance


  1. A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction, takes 4 seconds. The time taken by the trains to pass each other will be









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    Let the length of each train be x metres

    Then, Speed of first train =
    x
    m/sec
    3

    Speed of second train =
    x
    m/sec
    4

    They are moving in opposite directions
    ∴ Required time =
    x
    +
    x
    34

    =
    4x + 3x
    =
    7x
    m./sec.
    1212

    Total length = x + x = 2 x m.
    ∴  Time taken =
    2x
    7x
    12

    =
    24
    7

    = 3
    3
    sec.
    7

    Correct Option: B

    Let the length of each train be x metres

    Then, Speed of first train =
    x
    m/sec
    3

    Speed of second train =
    x
    m/sec
    4

    They are moving in opposite directions
    ∴ Required time =
    x
    +
    x
    34

    =
    4x + 3x
    =
    7x
    m./sec.
    1212

    Total length = x + x = 2 x m.
    ∴  Time taken =
    2x
    7x
    12

    =
    24
    7

    = 3
    3
    sec.
    7


  1. Two trains 108 m and 112 m in length are running towards each other on the parallel lines at a speed of 45 km/hr and 54 km/ hr respectively. To cross each other after they meet, it will take









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    Relative speed = 45 + 54 = 99 kmph

    = 99 ×
    5
    m/sec.
    18

    or  
    55
    m/sec.
    2

    ∴   Required time =
    108 + 112
    55
    2

    =
    220 × 2
    = 8 seconds
    55

    Correct Option: C

    Relative speed = 45 + 54 = 99 kmph

    = 99 ×
    5
    m/sec.
    18

    or  
    55
    m/sec.
    2

    ∴   Required time =
    108 + 112
    55
    2

    =
    220 × 2
    = 8 seconds
    55



  1. Two trains start from station A and B and travel towards each other at speed of 16 miles/ hour and 21 miles/ hour respectively. At the time of their meeting, the second train has travelled 60 miles more than the first. The distance between A and B (in miles) is :









  1. View Hint View Answer Discuss in Forum

    Let the trains meet after t hours
    Then, 21t – 16t = 60
    ⇒  5t = 60 ⇒ t = 12 hours
    ∴  Distance between A and B
    = (16 + 21) × 12
    = 37 × 12 = 444 miles
    Second Method :
    Here, a = 21, b = 16, d = 60

    Distance between A and B =
    a + b
    × d
    a − b

    =
    21 + 16
    × 60
    21 − 16

    =
    37
    × 60
    5

    = 37 × 12 = 444 miles

    Correct Option: A

    Let the trains meet after t hours
    Then, 21t – 16t = 60
    ⇒  5t = 60 ⇒ t = 12 hours
    ∴  Distance between A and B
    = (16 + 21) × 12
    = 37 × 12 = 444 miles
    Second Method :
    Here, a = 21, b = 16, d = 60

    Distance between A and B =
    a + b
    × d
    a − b

    =
    21 + 16
    × 60
    21 − 16

    =
    37
    × 60
    5

    = 37 × 12 = 444 miles


  1. Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 secs. If the speed of the second train is 43.2 km/hr, then the speed of the first train is









  1. View Hint View Answer Discuss in Forum

    Speed of second train
    = 43.2 kmph

    =
    43.2 × 5
    m/sec.
    18

    or 12 m/sec.Let the speed of first train be x m per second, then
    150 + 120
    = 10
    x + 12

    ⇒  27 = + x 12
    ⇒  x = 15 m/s
    = 15 ×
    18
    kmph = 54 kmph
    5

    Correct Option: A

    Speed of second train
    = 43.2 kmph

    =
    43.2 × 5
    m/sec.
    18

    or 12 m/sec.Let the speed of first train be x m per second, then
    150 + 120
    = 10
    x + 12

    ⇒  27 = + x 12
    ⇒  x = 15 m/s
    = 15 ×
    18
    kmph = 54 kmph
    5



  1. Two trains of length 137 metre and 163 metre are running with speed of 42 km/hr and 48 km/hr respectively towards each other on papallel tracks. In how many seconds will they cross each other?









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    Relative speed = 42 + 48 = 90 kmph

    =
    90 × 5
    m/s = 25 m/s
    18

    Sum of the length of both trains
    = 137 + 163 = 300 metres
    ∴  Required time =
    300
    = 12 seconds.
    25

    Correct Option: C

    Relative speed = 42 + 48 = 90 kmph

    =
    90 × 5
    m/s = 25 m/s
    18

    Sum of the length of both trains
    = 137 + 163 = 300 metres
    ∴  Required time =
    300
    = 12 seconds.
    25