Speed, Time and Distance


  1. A bus moving at 40 km per hour covers a distance in 6 hours 15 minutes. If it travels the same distance at 50 km per hour how long will it take to cover the distance ?
    1. 2 hrs.
    2. 6 hrs.
    3. 4 hrs.
    4. 5 hrs.

  1. View Hint View Answer Discuss in Forum

    Distance = Speed × TIme

    =
    40 × 6
    1
    km
    4

    =
    40 × 25
    km = 250 km
    4

    New speed = 50 kmph
    ∴  Required time
    =
    Distance
    =
    250
    = 5 hours
    Speed50


    Second Method :
    Here, S1 = 40, t1 = 6
    15
    =
    25
    604

    S2 = 50, t2 = ?
    S1t1 = S2t2
    40 ×
    25
    = 50 × t2
    4

    t2 = 5 hrs.

    Correct Option: D

    Distance = Speed × TIme

    =
    40 × 6
    1
    km
    4

    =
    40 × 25
    km = 250 km
    4

    New speed = 50 kmph
    ∴  Required time
    =
    Distance
    =
    250
    = 5 hours
    Speed50


    Second Method :
    Here, S1 = 40, t1 = 6
    15
    =
    25
    604

    S2 = 50, t2 = ?
    S1t1 = S2t2
    40 ×
    25
    = 50 × t2
    4

    t2 = 5 hrs.


  1. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at the rate 4 kmph and partly on bicycle at the rate 9 kmph. The distance travelled on foot is
    1. 16 km
    2. 14 km
    3. 17 km
    4. 15 km

  1. View Hint View Answer Discuss in Forum

    Distance travelled by farmer on foot = x km (let)
    ∴  Distance covered by cycling = (61–x ) km.

    Time =
    Distance
    Speed

    According to the question,
    x
    +
    61 − x
    = 9
    49

    ⇒ 
    9x + 61 × 4 − 4x
    = 9
    9 × 4

    ⇒  5x + 244 = 9 × 9 × 4 = 324
    ⇒  5x = 324 – 244 = 80
    ⇒  x =
    80
    = 16 km.
    5


    Second Method :
    Here, t = 9, x= 61
    u = 4, v = 9
    Time taken =
    vt − x
    v − u

    =
    9 × 9 − 61
    9 − 4

    =
    20
    = 4 hrs.
    5

    Distance travelled
    = 4 × 4 = 16 km

    Correct Option: A

    Distance travelled by farmer on foot = x km (let)
    ∴  Distance covered by cycling = (61–x ) km.

    Time =
    Distance
    Speed

    According to the question,
    x
    +
    61 − x
    = 9
    49

    ⇒ 
    9x + 61 × 4 − 4x
    = 9
    9 × 4

    ⇒  5x + 244 = 9 × 9 × 4 = 324
    ⇒  5x = 324 – 244 = 80
    ⇒  x =
    80
    = 16 km.
    5


    Second Method :
    Here, t = 9, x= 61
    u = 4, v = 9
    Time taken =
    vt − x
    v − u

    =
    9 × 9 − 61
    9 − 4

    =
    20
    = 4 hrs.
    5

    Distance travelled
    = 4 × 4 = 16 km



  1. The distance between 2 places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/h towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is
    1. 18 km/hour
    2. 6 km/hour
    3. 20 km/hour
    4. 8 km/hour
    5. None of these

  1. View Hint View Answer Discuss in Forum

    Speed of Romita = x kmph
    (let)
    Distance = Speed × Time
    According to the question,
    4 × 6 + x × 6 = 42
    ⇒  6x = 42 – 24 = 18
    ⇒  x = 18 ÷ 6 = 3 kmph
    Second Method :
    Distance from R to S = S1t1+S2t2
    42 = 4 × 6 + x × 6
    6x = 18 x = 3 km/hr.

    Correct Option: E

    Speed of Romita = x kmph
    (let)
    Distance = Speed × Time
    According to the question,
    4 × 6 + x × 6 = 42
    ⇒  6x = 42 – 24 = 18
    ⇒  x = 18 ÷ 6 = 3 kmph
    Second Method :
    Distance from R to S = S1t1+S2t2
    42 = 4 × 6 + x × 6
    6x = 18 x = 3 km/hr.


  1. A journey takes 4 hours 30 minutes at a speed of 60 km/hr. If the speed is 15 m/s, then the
    journey will take
    1. 5 hours
    2. 5 hours 30 minutes
    3. 6 hours
    4. 6 hours 15 minutes

  1. View Hint View Answer Discuss in Forum

    60 kmph =
    60 × 5
    m/sec
    18

    =
    50
    m/sec.
    3

    ∴  Speed ∝
    1
    Time

    ⇒  S1 × T1 = S2 × T2
    ⇒ 
    50
    ×
    9
    = 15 × T2
    32

    ⇒  T2 =
    75
    = 5 hours
    15


    Second Method :
    Here, S1 = 60, t1 = 4
    1
    =
    9
    22

    S2 = 15 ×
    18
    = 54
    5

    S1t1 = S2t2
    60 ×
    9
    = 54 × t2
    2

    t2 =
    270
    = 5 hours
    54

    Correct Option: A

    60 kmph =
    60 × 5
    m/sec
    18

    =
    50
    m/sec.
    3

    ∴  Speed ∝
    1
    Time

    ⇒  S1 × T1 = S2 × T2
    ⇒ 
    50
    ×
    9
    = 15 × T2
    32

    ⇒  T2 =
    75
    = 5 hours
    15


    Second Method :
    Here, S1 = 60, t1 = 4
    1
    =
    9
    22

    S2 = 15 ×
    18
    = 54
    5

    S1t1 = S2t2
    60 ×
    9
    = 54 × t2
    2

    t2 =
    270
    = 5 hours
    54



  1. Sriya with her family travelled from Bolpur to Suri by car at a speed of 40 km/hr and returned to Bolpur at a speed of 50 km/hr. The average speed for the whole journey is
    1. 44
      4
      km/hr
      9
    2. 45 km/hr
    3. 45
      1
      km/hr
      2
    4. 44.78 km/hr

  1. View Hint View Answer Discuss in Forum

    Average speed of journey =
    2xy
    kmph
    x + y

    ⇒ 
    2 × 40 × 50
    =
    2 × 40 × 50
    40 + 5090

    ⇒ 
    400
    = 44
    4
    kmph
    99

    Correct Option: A

    Average speed of journey =
    2xy
    kmph
    x + y

    ⇒ 
    2 × 40 × 50
    =
    2 × 40 × 50
    40 + 5090

    ⇒ 
    400
    = 44
    4
    kmph
    99