Speed, Time and Distance


  1. A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at
    1. 8:36 am
    2. 8:56 am
    3. 9:00 am
    4. 9:24 am

  1. View Hint View Answer Discuss in Forum

    Let both trains meet after t hours since 7 a.m.
    Distance between stations A and B = x Km.

    ∴ 
    x
    × t +
    x
    × (t − 1) = x
    47/2

    Speed =
    Distance
    Time

    ⇒  
    t
    +
    2(t − 1)
    = 1
    47

    ⇒  
    7t + 8t − 8
    = 1
    28

    ⇒  15 t – 8 = 28
    ⇒  15 t = 28 + 8 = 36
    ⇒   t =
    36
    =
    12
    hours
    155

    = 2 hours 24 minutes
    ∴  Required time = 9 :24 a.m.

    Correct Option: D

    Let both trains meet after t hours since 7 a.m.
    Distance between stations A and B = x Km.

    ∴ 
    x
    × t +
    x
    × (t − 1) = x
    47/2

    Speed =
    Distance
    Time

    ⇒  
    t
    +
    2(t − 1)
    = 1
    47

    ⇒  
    7t + 8t − 8
    = 1
    28

    ⇒  15 t – 8 = 28
    ⇒  15 t = 28 + 8 = 36
    ⇒   t =
    36
    =
    12
    hours
    155

    = 2 hours 24 minutes
    ∴  Required time = 9 :24 a.m.


  1. A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is
    1. 400
    2. 300
    3. 200
    4. 500

  1. View Hint View Answer Discuss in Forum

    Speed of train = 60 kmph

    =60 ×
    5
    m/sec.
    18

    =
    50
    m/sec.
    3

    If the length of platform be = x metre, then
    ∴  Speed of train =
    Length of (train + platform)
    Time taken in crossing

    ⇒ 
    50
    =
    200 + x
    330

    ⇒  50 × 10 = 200 + x
    ⇒  x = 500 – 200 = 300 metre

    Correct Option: B

    Speed of train = 60 kmph

    =60 ×
    5
    m/sec.
    18

    =
    50
    m/sec.
    3

    If the length of platform be = x metre, then
    ∴  Speed of train =
    Length of (train + platform)
    Time taken in crossing

    ⇒ 
    50
    =
    200 + x
    330

    ⇒  50 × 10 = 200 + x
    ⇒  x = 500 – 200 = 300 metre



  1. A train moving at a rate of 36 km/hr. crosses a standing man in 10 seconds. It will cross a platform 55 metres long, in :
    1. 6 seconds
    2. 7 seconds
    3. 15
      1
      seconds
      2
    4. 5
      1
      seconds
      2

  1. View Hint View Answer Discuss in Forum

    Speed of train = 36 kmph

    = 36 ×
    5
    = 10 m/sec
    18

    Length of train = 10 × 10 = 100 metres
    ∴  Required time =
    100 + 55
    10

    = 15
    5
    = 15
    1
    second
    102

    = 15.5 seconds

    Correct Option: C

    Speed of train = 36 kmph

    = 36 ×
    5
    = 10 m/sec
    18

    Length of train = 10 × 10 = 100 metres
    ∴  Required time =
    100 + 55
    10

    = 15
    5
    = 15
    1
    second
    102

    = 15.5 seconds


  1. A train passes by a lamp post on a platform in 7 sec. and passes by the platform completely in 28 sec. If the length of the platform is 390 m, then length of the train (in metres) is
    1. 120
    2. 130
    3. 140
    4. 150

  1. View Hint View Answer Discuss in Forum

    Let the length of train be x metre, then

    ∴  Speed of train =
    x
    =
    x + 390
    728

    ⇒  x =
    x + 390
    4

    ⇒  4x – x = 390
    ⇒  x =
    390
    = 130 metres
    3

    Correct Option: B

    Let the length of train be x metre, then

    ∴  Speed of train =
    x
    =
    x + 390
    728

    ⇒  x =
    x + 390
    4

    ⇒  4x – x = 390
    ⇒  x =
    390
    = 130 metres
    3



  1. Two trains 100 metres and 95 metres long respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are
    1. 44 km/hr, 22 km/hr
    2. 52 km/hr, 26 km/hr
    3. 36 km/hr. 18 km/hr
    4. 40 km/hr, 20 km/hr

  1. View Hint View Answer Discuss in Forum

    Let the speed of trains be x and y metre/sec respectively,

    100 + 95
    = 27
    x − y

    ⇒  x − y =
    195
    =
    65
       .....(i)
    279

    Again,
    195
    = 9
    x + y

    ⇒  x + y =
    195
       .....(ii)
    9

    By equation (i) + (ii)
    ⇒  2x =
    65
    +
    195
    =
    260
    999

    ⇒  x =
    260
    =
    130
    m/sec.
    2 × 99

    =
    130
    ×
    18
    kmph = 52 kmph
    95

    From equation (ii),
    y =
    195
    130
    =
    65
    m/sec.
    999

    =
    65
    ×
    18
    = 26 kmph
    95

    Correct Option: B

    Let the speed of trains be x and y metre/sec respectively,

    100 + 95
    = 27
    x − y

    ⇒  x − y =
    195
    =
    65
       .....(i)
    279

    Again,
    195
    = 9
    x + y

    ⇒  x + y =
    195
       .....(ii)
    9

    By equation (i) + (ii)
    ⇒  2x =
    65
    +
    195
    =
    260
    999

    ⇒  x =
    260
    =
    130
    m/sec.
    2 × 99

    =
    130
    ×
    18
    kmph = 52 kmph
    95

    From equation (ii),
    y =
    195
    130
    =
    65
    m/sec.
    999

    =
    65
    ×
    18
    = 26 kmph
    95