Speed, Time and Distance


  1. How much time does a train, 50 m long, moving at 68 km/ hour take to pass another train, 75 m long, moving at 50 km/hour in the same direction ?
    1. 5 seconds
    2. 10 seconds
    3. 20 seconds
    4. 25 seconds

  1. View Hint View Answer Discuss in Forum

    Both trains are moving in the same direction.
    ∴  Their relative speed
    = (68 – 50) kmph = 18 kmph

    = 18 ×
    5
    = 5 m/sec
    8

    Total length = 50 + 75 = 125 m
    ∴   Required time =
    Total length
    Relative speed

    =
    125
    = 25 seconds.
    5

    Correct Option: D

    Both trains are moving in the same direction.
    ∴  Their relative speed
    = (68 – 50) kmph = 18 kmph

    = 18 ×
    5
    = 5 m/sec
    8

    Total length = 50 + 75 = 125 m
    ∴   Required time =
    Total length
    Relative speed

    =
    125
    = 25 seconds.
    5


  1. A constable is 114 metres behind a thief. The constable runs 21 metres and the thief runs 15
    metres in a minute. In what time will the constable catch the thief ?
    1. 19 minutes
    2. 18 minutes
    3. 17 minutes
    4. 16 minutes

  1. View Hint View Answer Discuss in Forum

    The gap of 114 metre will be filled at relative speed.

    Required time =
    114
    minutes
    21 − 15

    =
    114
    = 19 minutes
    6

    Correct Option: A

    The gap of 114 metre will be filled at relative speed.

    Required time =
    114
    minutes
    21 − 15

    =
    114
    = 19 minutes
    6



  1. A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?
    1. 85 km/hr.
    2. 50 km/hr.
    3. 55 km/hr.
    4. 25 km/hr.

  1. View Hint View Answer Discuss in Forum

    Suppose the speed of first train be x kmph
    Speed of second train = 30 kmph

    =
    3 × 1000
    = 500 m per min.
    60

    ∴  According to question
    Total Distance
    Relative speed

    =
    (66 + 88)
    = 0.168
    x − 500

    ⇒ 
    154
    = 0.168
    x − 500

    ⇒  0.168x – 84 = 154
    ⇒  0.168x = 238
    ⇒  x =
    238
    0.168

    =
    238 × 1000
    m per minute
    168

    =
    238 × 1000
    ×
    3
    kmph
    16850

    = 85 kmph

    Correct Option: A

    Suppose the speed of first train be x kmph
    Speed of second train = 30 kmph

    =
    3 × 1000
    = 500 m per min.
    60

    ∴  According to question
    Total Distance
    Relative speed

    =
    (66 + 88)
    = 0.168
    x − 500

    ⇒ 
    154
    = 0.168
    x − 500

    ⇒  0.168x – 84 = 154
    ⇒  0.168x = 238
    ⇒  x =
    238
    0.168

    =
    238 × 1000
    m per minute
    168

    =
    238 × 1000
    ×
    3
    kmph
    16850

    = 85 kmph


  1. A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km./hr and 11 km./hr respectively. What is the distance between them after 6 minutes ?
    1. 100 m
    2. 190 m
    3. 200 m
    4. 150 m

  1. View Hint View Answer Discuss in Forum

    Relative speed of police
    = 11 – 10 = 1 kmph

    =
    5
    m/sec
    18

    ∴  Distance decreased in 6 minutes =
    5
    × 6 × 60
    18

    = 100 m
    ∴  Distance remained between them = 200–100 = 100 m

    Correct Option: A

    Relative speed of police
    = 11 – 10 = 1 kmph

    =
    5
    m/sec
    18

    ∴  Distance decreased in 6 minutes =
    5
    × 6 × 60
    18

    = 100 m
    ∴  Distance remained between them = 200–100 = 100 m



  1. The speeds of three cars are in the ratio of 1 : 3 : 5. The ratio among the time taken by these cars to travel the same distance is
    1. 3 : 5 : 15
    2. 15 : 3 : 5
    3. 15 : 5 : 3
    4. 5 : 3 : 1

  1. View Hint View Answer Discuss in Forum

    Speed ∝
    1
    Time

    ∴   Required ratio of time = 1 :
    1
    :
    1
    35

    = 15 :
    1
    × 15 :
    1
    × 15
    35

    = 15 : 5 : 3

    Correct Option: C

    Speed ∝
    1
    Time

    ∴   Required ratio of time = 1 :
    1
    :
    1
    35

    = 15 :
    1
    × 15 :
    1
    × 15
    35

    = 15 : 5 : 3