Speed, Time and Distance


  1. Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is









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    Speed of train starting from Q = x kmph
    ∴  Speed of train starting from P = (x + 8) kmph
    According to the question,
    PR + RQ = PQ
    ⇒  (x + 8) × 6 + x × 6 = 162
    [Distance = Speed × Time]
    ⇒  6x + 48 + 6x = 162
    ⇒  12x = 162 – 48 = 114

    ⇒  x =
    114
    =
    19
    122

    = 9
    1
    kmph
    2

    Correct Option: C


    Speed of train starting from Q = x kmph
    ∴  Speed of train starting from P = (x + 8) kmph
    According to the question,
    PR + RQ = PQ
    ⇒  (x + 8) × 6 + x × 6 = 162
    [Distance = Speed × Time]
    ⇒  6x + 48 + 6x = 162
    ⇒  12x = 162 – 48 = 114

    ⇒  x =
    114
    =
    19
    122

    = 9
    1
    kmph
    2


  1. P and Q starting simultaneously from two different places proceed towards each other at a speed of 20 km/hour and 30 km/hour respectively. By the time they meet each other. Q has covered 36 km more than that of P. The distance (in km.) between the two places is









  1. View Hint View Answer Discuss in Forum

    Let P and Q meet after t hours.
    Distance = speed × time
    According to the question,
    30t – 20t = 36
    ⇒  10t = 36

    ⇒  t =
    36
    = 3.6 hours
    10

    ∴  Distance between P and Q
    = 30t + 20t
    = 50t = (50 × 3.6) km.
    = 180 km.

    Second Method :
    Here, a = 30, b = 20, d = 36
    Required distance =
    a + b
    × d
    a − b

    =
    30 + 20
    × 36
    30 − 20

    =
    50
    × 36 = 180 km
    10

    Correct Option: C

    Let P and Q meet after t hours.
    Distance = speed × time
    According to the question,
    30t – 20t = 36
    ⇒  10t = 36

    ⇒  t =
    36
    = 3.6 hours
    10

    ∴  Distance between P and Q
    = 30t + 20t
    = 50t = (50 × 3.6) km.
    = 180 km.

    Second Method :
    Here, a = 30, b = 20, d = 36
    Required distance =
    a + b
    × d
    a − b

    =
    30 + 20
    × 36
    30 − 20

    =
    50
    × 36 = 180 km
    10



  1. Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is









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    Speed of X
    Speed of Y

    =
    Time taken by Y
    Time taken by X

    ⇒ 
    45
    =
    3 hours 20 min.
    y4 hours 48 min.

    ⇒ 
    45
    =
    200 minutes
    y288 minutes

    =
    10
    12

    ⇒  10y = 12 × 45
    ⇒  y =
    12 × 45
    = 54 kmph
    10

    Correct Option: C

    Speed of X
    Speed of Y

    =
    Time taken by Y
    Time taken by X

    ⇒ 
    45
    =
    3 hours 20 min.
    y4 hours 48 min.

    ⇒ 
    45
    =
    200 minutes
    y288 minutes

    =
    10
    12

    ⇒  10y = 12 × 45
    ⇒  y =
    12 × 45
    = 54 kmph
    10


  1. A train running at the speed of 84 km/hr passes a man walking in opposite direction at the
    speed of 6 km/hr in 4 seconds. What is the length of train (in metre) ?









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    Relative speed = (84 + 6) = 90 kmph

    = 90 ×
    5
    m/sec.
    18

    = 25 m/sec.
    ∴  Length of train
    = Relative speed × Time
    = 25 × 4 = 100 metre

    Correct Option: C

    Relative speed = (84 + 6) = 90 kmph

    = 90 ×
    5
    m/sec.
    18

    = 25 m/sec.
    ∴  Length of train
    = Relative speed × Time
    = 25 × 4 = 100 metre



  1. Two trains, each of length 125 metre, are running in parallel tracks in opposite directions. One train is running at a speed 65 km/hour and they cross each other in 6 seconds. The speed of the other train is









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    Total length of both trains = 250 metres
    Let speed of second train =x kmph
    Relative speed = (65 + x) kmph

    = (65 + x) ×
    5
    m/sec
    18

    ∴ Time =
    Sum of length of trains
    Relative Speed

    ⇒ 6 =
    250
    (65 + x) ×
    5
    18

    ⇒  6 ×
    5
    × (65 + x) = 250
    18

    ⇒  65 + x =
    250 × 3
    5

    ⇒  65 + x = 150
    ⇒  x = 150 – 65 = 85 kmph

    Correct Option: B

    Total length of both trains = 250 metres
    Let speed of second train =x kmph
    Relative speed = (65 + x) kmph

    = (65 + x) ×
    5
    m/sec
    18

    ∴ Time =
    Sum of length of trains
    Relative Speed

    ⇒ 6 =
    250
    (65 + x) ×
    5
    18

    ⇒  6 ×
    5
    × (65 + x) = 250
    18

    ⇒  65 + x =
    250 × 3
    5

    ⇒  65 + x = 150
    ⇒  x = 150 – 65 = 85 kmph