Speed, Time and Distance


  1. Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes, the slower train in 36 seconds. The length of each train is :
    1. 82 m
    2. 50 m
    3. 80 m
    4. 72 m

  1. View Hint View Answer Discuss in Forum

    Let the length of each train be x metre.
    Relative speed = 46 – 36 = 10 kmph

    =
    10 × 5
    metre/second
    18

    =
    25
    metre/second
    9

    ∴  
    2x
    = 36
    (25/9)

    ⇒  2x =
    36 × 25
    = 100
    9

    ⇒  x = 50 metre

    Correct Option: B

    Let the length of each train be x metre.
    Relative speed = 46 – 36 = 10 kmph

    =
    10 × 5
    metre/second
    18

    =
    25
    metre/second
    9

    ∴  
    2x
    = 36
    (25/9)

    ⇒  2x =
    36 × 25
    = 100
    9

    ⇒  x = 50 metre


  1. A bus moving at a speed of 45 km/hr overtakes a truck 150 metres ahead going in the same direction in 30 seconds. The speed of the truck is
    1. 27 km/hr
    2. 24 km/hr
    3. 25 km/hr
    4. 28 km/hr

  1. View Hint View Answer Discuss in Forum

    Let the speed of the truck be x kmph
    Relative speed of the bus = (45 - x) kmph

    ∴   Time =
    Distance
    Relative speed

    ⇒ 
    30
    60 × 60

    =
    150
    1000
    (45 − x)

    ⇒ 
    1
    =
    15
    120100(45 − x)

    ⇒ 
    1
    =
    3
    ⇒ (45 − x) = 18
    6(45 − x)

    ⇒  x = 45 – 18 = 27 kmph

    Correct Option: A

    Let the speed of the truck be x kmph
    Relative speed of the bus = (45 - x) kmph

    ∴   Time =
    Distance
    Relative speed

    ⇒ 
    30
    60 × 60

    =
    150
    1000
    (45 − x)

    ⇒ 
    1
    =
    15
    120100(45 − x)

    ⇒ 
    1
    =
    3
    ⇒ (45 − x) = 18
    6(45 − x)

    ⇒  x = 45 – 18 = 27 kmph



  1. Two trains travel in the same direction at the speed of 56 km/h and 29 km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is
    1. 100
    2. 80
    3. 75
    4. 120

  1. View Hint View Answer Discuss in Forum

    Relative speed = 56 – 29 = 27 kmph

    = 27 ×
    5
    =
    15
    m/sec
    182

    ∴  Distance covered in 10 seconds
    =
    15
    × 10 = 75 m
    2

    Hence, length of train = 75 m.

    Correct Option: C

    Relative speed = 56 – 29 = 27 kmph

    = 27 ×
    5
    =
    15
    m/sec
    182

    ∴  Distance covered in 10 seconds
    =
    15
    × 10 = 75 m
    2

    Hence, length of train = 75 m.


  1. Two trains are running with speed 30 km/hr and 58 km/hr in the same direction. A man in
    the slower train passes the faster train in 18 seconds. The length (in metres) of the faster train is :
    1. 70
    2. 100
    3. 128
    4. 140

  1. View Hint View Answer Discuss in Forum

    Relative speed = (58 – 30) km/hr

    = 28 ×
    5
    m/sec.
    18

    =
    70
    m/sec.
    9

    ∴   Length of train =
    70
    × 18
    9

    = 140 metres

    Correct Option: D

    Relative speed = (58 – 30) km/hr

    = 28 ×
    5
    m/sec.
    18

    =
    70
    m/sec.
    9

    ∴   Length of train =
    70
    × 18
    9

    = 140 metres



  1. A constable follows a thief who is 200 m ahead of the constable. If the constable and the thief run at speed of 8 km/hour and 7 km/hour respectively, the constable would catch the thief in
    1. 10 minutes
    2. 12 minutes
    3. 15 minutes
    4. 20 minutes

  1. View Hint View Answer Discuss in Forum

    The constable and thief are running in the same direction
    ∴   Their relative speed = 8 – 7 = 1km.

    = 1 ×
    5
    m/sec.
    18

    ∴ 
    Required time =
    200
    5
    18

    =
    200 × 18
    = 720 sec
    5

    =
    720
    minutes = 12 minutes
    60

    Correct Option: B

    The constable and thief are running in the same direction
    ∴   Their relative speed = 8 – 7 = 1km.

    = 1 ×
    5
    m/sec.
    18

    ∴ 
    Required time =
    200
    5
    18

    =
    200 × 18
    = 720 sec
    5

    =
    720
    minutes = 12 minutes
    60