Speed, Time and Distance


  1. A train, 150 m long, takes 30 seconds to cross a bridge 500 m long. How much time will the train take to cross a platform 370 m long ?
    1. 36 secs
    2. 30 secs
    3. 24 secs
    4. 18 secs

  1. View Hint View Answer Discuss in Forum

    When a train croses a bridge, distance covered = length of (bridge + train).

    ∴  Speed of train =
    150 + 500
    30

    =
    650
    =
    65
    m/sec.
    303

    ∴ Time taken to cross the 370m long platform
    =
    370 + 150
    65
    3

    =
    520 × 3
    = 24 seconds
    65

    Correct Option: C

    When a train croses a bridge, distance covered = length of (bridge + train).

    ∴  Speed of train =
    150 + 500
    30

    =
    650
    =
    65
    m/sec.
    303

    ∴ Time taken to cross the 370m long platform
    =
    370 + 150
    65
    3

    =
    520 × 3
    = 24 seconds
    65


  1. A train takes 18 seconds to pass through a platform 162 m long and 15 seconds to pass through another platform 120 m long. The length of the train (in m) is :
    1. 70
    2. 80
    3. 90
    4. 105

  1. View Hint View Answer Discuss in Forum

    Let the length of the train be x metres.
    When a train corsses a platform it covers a distance equal to the sum of lengths of train and platform. Also, the speed of train is same.

    ∴ 
    x + 162
    =
    x + 120
    1815

    ⇒  6x + 720 = 5x + 810
    ⇒  6x – 5x = 810 – 720
    ⇒  x = 90
    ∴  The length of the train = 90m.

    Correct Option: C

    Let the length of the train be x metres.
    When a train corsses a platform it covers a distance equal to the sum of lengths of train and platform. Also, the speed of train is same.

    ∴ 
    x + 162
    =
    x + 120
    1815

    ⇒  6x + 720 = 5x + 810
    ⇒  6x – 5x = 810 – 720
    ⇒  x = 90
    ∴  The length of the train = 90m.



  1. A train is moving at a speed of 132 km/hour. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
    1. 5 seconds
    2. 7.5 seconds
    3. 10 seconds
    4. 15 seconds

  1. View Hint View Answer Discuss in Forum

    When a train crosses a railway platform, it travels a distance equal to sum of length of platform and its own length.
    Speed = 132 kmph

    = 132 ×
    5
    =
    110
    m/sec
    183

    ∴  Required time


    =
    110 + 165
    seconds
    110
    3

    =
    275 × 3
    = 7.5 seconds
    110


    Second Method :
    Here, x = 110m,
    u = 132 km/hr.
    = 132 ×
    5
    =
    110
    m/sec
    183

    y = 165m, t = ?
    using
    t =
    x + y
    u


    t =
    110 + 165
    110
    3

    t =
    275 × 3
    110

    =
    25 × 3
    =
    15
    = 7.5 sec
    102

    Correct Option: B

    When a train crosses a railway platform, it travels a distance equal to sum of length of platform and its own length.
    Speed = 132 kmph

    = 132 ×
    5
    =
    110
    m/sec
    183

    ∴  Required time


    =
    110 + 165
    seconds
    110
    3

    =
    275 × 3
    = 7.5 seconds
    110


    Second Method :
    Here, x = 110m,
    u = 132 km/hr.
    = 132 ×
    5
    =
    110
    m/sec
    183

    y = 165m, t = ?
    using
    t =
    x + y
    u


    t =
    110 + 165
    110
    3

    t =
    275 × 3
    110

    =
    25 × 3
    =
    15
    = 7.5 sec
    102


  1. A train 800 metres long is running at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :
    1. 77200
    2. 500
    3. 1300
    4. 13

  1. View Hint View Answer Discuss in Forum

    When a train crosses a tunnel, it covers a distance equal to the sum of its own length and
    tunnel.
    Let the length of tunnel be x
    Speed = 78 kmph

    =
    78 × 1000
    m/sec. =
    65
    m/sec.
    60 × 603

    ∴  Speed =
    Distance
    Time

    ⇒ 
    65
    =
    800 + x
    360

    ⇒  (800 + x ) × 3 = 65× 60
    ⇒  800 + x = 65 × 20 m
    ⇒  x = 1300 – 800 = 500
    ∴  Length of tunnel = 500 metres.

    Second Method :
    Here, x = 800 m,
    u = 78 km/hr
    = 78
    5
    =
    65
    m/sec
    183

    t = 1 min = 60 sec, y = ?
    using
    t =
    x + y
    u


    60 =
    800 + y
    65
    3

    60 ×
    65
    = 800 + y
    3

    1300 – 800 = y
    y = 500 metres

    Correct Option: B

    When a train crosses a tunnel, it covers a distance equal to the sum of its own length and
    tunnel.
    Let the length of tunnel be x
    Speed = 78 kmph

    =
    78 × 1000
    m/sec. =
    65
    m/sec.
    60 × 603

    ∴  Speed =
    Distance
    Time

    ⇒ 
    65
    =
    800 + x
    360

    ⇒  (800 + x ) × 3 = 65× 60
    ⇒  800 + x = 65 × 20 m
    ⇒  x = 1300 – 800 = 500
    ∴  Length of tunnel = 500 metres.

    Second Method :
    Here, x = 800 m,
    u = 78 km/hr
    = 78
    5
    =
    65
    m/sec
    183

    t = 1 min = 60 sec, y = ?
    using
    t =
    x + y
    u


    60 =
    800 + y
    65
    3

    60 ×
    65
    = 800 + y
    3

    1300 – 800 = y
    y = 500 metres



  1. A train 300 metres long is running at a speed of 25 metres per second. It will cross a bridge of 200 metres in
    1. 5 seconds
    2. 10 seconds
    3. 20 seconds
    4. 25 seconds

  1. View Hint View Answer Discuss in Forum

    In crossing the bridge, the train travels its own length plus the length of the bridge.
    Total distance (length)
    = 300 + 200 = 500 m.
    Speed = 25m/sec.
    ∴  The required time
    = 500 ÷ 25 = 20 seconds
    Second Method :
    Here, x = 300m, y= 200 m, t = ?
    u= 25 m/sec

    t =
    x + y
    u

    =
    300 + 200
    25

    =
    500
    25

    t = 20 seconds

    Correct Option: C

    In crossing the bridge, the train travels its own length plus the length of the bridge.
    Total distance (length)
    = 300 + 200 = 500 m.
    Speed = 25m/sec.
    ∴  The required time
    = 500 ÷ 25 = 20 seconds
    Second Method :
    Here, x = 300m, y= 200 m, t = ?
    u= 25 m/sec

    t =
    x + y
    u

    =
    300 + 200
    25

    =
    500
    25

    t = 20 seconds