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. 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. 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. 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. 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. 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