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
    1. 12
      5
      km/hour
      6
    2. 10
      5
      km/hour
      6
    3. 9
      1
      km/hour
      2
    4. 8
      1
      km/hour
      2

  1. View Hint View Answer Discuss in Forum


    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. 144
    2. 162
    3. 180
    4. 108

  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
    1. 60 km/hr
    2. 58 km/hr
    3. 54 km/hr
    4. 64.8 km/hr

  1. View Hint View Answer Discuss in Forum

    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) ?
    1. 150
    2. 120
    3. 100
    4. 90

  1. View Hint View Answer Discuss in Forum

    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
    1. 75 km/hour
    2. 85 km/hour
    3. 95 km/hour
    4. 105 km/hour

  1. View Hint View Answer Discuss in Forum

    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