Speed, Time and Distance


  1. Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in
    1. 14.4 seconds
    2. 15.5 seconds
    3. 18.8 seconds
    4. 20.2 seconds

  1. View Hint View Answer Discuss in Forum

    Let the length of each train be x metre.

    Speed of first train =
    x
    m/sec
    18

    Speed of second train =
    x
    m/sec
    12

    When both trains cross each other, time taken
    =
    2x
    x
    +
    x
    1812


    =
    2x
    2x + 3x
    36

    =
    2x × 36
    5x

    =
    72
    = 14.4 seconds
    5

    Correct Option: A

    Let the length of each train be x metre.

    Speed of first train =
    x
    m/sec
    18

    Speed of second train =
    x
    m/sec
    12

    When both trains cross each other, time taken
    =
    2x
    x
    +
    x
    1812


    =
    2x
    2x + 3x
    36

    =
    2x × 36
    5x

    =
    72
    = 14.4 seconds
    5


  1. Two trains 105 metres and 90 metres long, runs at the speed of 45 km/hr and 72 km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is
    1. 8 seconds
    2. 6 seconds
    3. 7 seconds
    4. 5 seconds

  1. View Hint View Answer Discuss in Forum

    Length of both trains
    = 105 + 90 = 195 m.
    Relative speed = (45 + 72) = 117 kmph

    = 117 ×
    5
    or
    65
    m/sec.
    182

    ∴  Time taken =
    195
    65
    2

    =
    195 × 2
    = 6 seconds
    65

    Correct Option: B

    Length of both trains
    = 105 + 90 = 195 m.
    Relative speed = (45 + 72) = 117 kmph

    = 117 ×
    5
    or
    65
    m/sec.
    182

    ∴  Time taken =
    195
    65
    2

    =
    195 × 2
    = 6 seconds
    65



  1. Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is
    1. 100 km/hr
    2. 120 km/hr
    3. 140 km/hr
    4. 150 km/hr

  1. View Hint View Answer Discuss in Forum

    Let the speed of second train be x m/s.

    80 km/h =
    80 × 5
    m/s
    18

    According to the question
    1000
    = 18
    x +
    80 × 5
    18

    ⇒  1000 = 18x + 400
    ∴  x =
    600
    m/s
    18

    =
    600
    ×
    18
    km/h = 120 km/h
    185

    Correct Option: B

    Let the speed of second train be x m/s.

    80 km/h =
    80 × 5
    m/s
    18

    According to the question
    1000
    = 18
    x +
    80 × 5
    18

    ⇒  1000 = 18x + 400
    ∴  x =
    600
    m/s
    18

    =
    600
    ×
    18
    km/h = 120 km/h
    185


  1. Two trains start from stations A and B and travel towards each other at speed of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is :
    1. 990 km
    2. 1200 km
    3. 1320 km
    4. 1440 km

  1. View Hint View Answer Discuss in Forum

    Let train A start from station A and B from station B.
    Let the trains A and B meet after t hours.
    ∴  Distance covered by train A in t hours = 50t
    Distance covered by train B in t hours = 60t km
    According to the question,
    60t – 50t = 120

    ⇒  t =
    120
    = 12 hours.
    10

    ∴  Distance AB = 50 × 12 + 60 ×
    12 = 600 + 720 = 1320 km
    Second Method :
    Here, a = 60, b = 50, d = 120
    Distance between A and B =
    a + b
    × d
    a − b

       =
    60 + 50
    × 120
    60 − 50

    =
    110
    × 120 = 1320 km
    10

    Correct Option: C

    Let train A start from station A and B from station B.
    Let the trains A and B meet after t hours.
    ∴  Distance covered by train A in t hours = 50t
    Distance covered by train B in t hours = 60t km
    According to the question,
    60t – 50t = 120

    ⇒  t =
    120
    = 12 hours.
    10

    ∴  Distance AB = 50 × 12 + 60 ×
    12 = 600 + 720 = 1320 km
    Second Method :
    Here, a = 60, b = 50, d = 120
    Distance between A and B =
    a + b
    × d
    a − b

       =
    60 + 50
    × 120
    60 − 50

    =
    110
    × 120 = 1320 km
    10



  1. Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :
    1. 10 sec.
    2. 10.8 sec.
    3. 9 sec.
    4. 9.6 sec.

  1. View Hint View Answer Discuss in Forum

    Total length of trains
    = 140 + 160 = 300 m.
    Relative speed = 60 + 40 = 100 kmph

    = 100 ×
    5
    m/sec.
    18

    or 
    250
    m/sec.
    9

    ∴  Time taken to cross each other
    =
    300
    250
    9

    =
    300 × 9
    = 10.8 sec.
    250

    Correct Option: B

    Total length of trains
    = 140 + 160 = 300 m.
    Relative speed = 60 + 40 = 100 kmph

    = 100 ×
    5
    m/sec.
    18

    or 
    250
    m/sec.
    9

    ∴  Time taken to cross each other
    =
    300
    250
    9

    =
    300 × 9
    = 10.8 sec.
    250