Speed, Time and Distance


  1. A car travels from A to B at the rate of 40 km/h and returns from B to A at the rate of 60 km/h. Its average speed during the whole journey is
    1. 48 km/h
    2. 50 km/h
    3. 45 km/h
    4. 60 km/h

  1. View Hint View Answer Discuss in Forum

    Here, distance is same.

    ∴  Average speed =
    2xy
    x + y

    =
    2 × 40 × 60
    kmph.
    40 + 60

    =
    2 × 40 × 60
    kmph.
    100

    = 48 kmph.

    Correct Option: A

    Here, distance is same.

    ∴  Average speed =
    2xy
    x + y

    =
    2 × 40 × 60
    kmph.
    40 + 60

    =
    2 × 40 × 60
    kmph.
    100

    = 48 kmph.


  1. Gautam travels 160 kms at 32 kmph and returns at 40 kmph. Then his average speed is
    1. 72 kmph
    2. 71.11 kmph
    3. 36 kmph
    4. 35.55 kmph

  1. View Hint View Answer Discuss in Forum

    Here, distances are equal.

    ∴  Average speed =
    2xy
    kmph.
    x + y

    =
    2 × 32 × 40
    kmph.
    32 + 40

    =
    2 × 32 × 40
    kmph.
    72

    =
    320
    kmph. = 35.55 kmph.
    9

    Correct Option: D

    Here, distances are equal.

    ∴  Average speed =
    2xy
    kmph.
    x + y

    =
    2 × 32 × 40
    kmph.
    32 + 40

    =
    2 × 32 × 40
    kmph.
    72

    =
    320
    kmph. = 35.55 kmph.
    9



  1. Durga walks 5 km from her home to school in 60 minutes, then bicycles back to home along the same route at 15 km per hour. Her sister Smriti makes the same round trip, but does so at half of Durga’s average speed. How much time does Smriti spend on her round trip ?
    1. 120 minutes
    2. 40 minutes
    3. 160 minutes
    4. 80 minutes

  1. View Hint View Answer Discuss in Forum

    Durga’s average speed =
    2xy
    kmph.
    x + y
    =
    2 × 5 × 15
    kmph
    20

    =
    15
    kmph
    2

    Distance of School = 5 km.
    ∴  Required time = 2
    5
    hours
    15/4

    =
    2 × 5 × 4
    hours
    15

    =
    8
    hours
    3

    =
    8
    × 60 minutes
    3

    = 160 minutes

    Correct Option: C

    Durga’s average speed =
    2xy
    kmph.
    x + y
    =
    2 × 5 × 15
    kmph
    20

    =
    15
    kmph
    2

    Distance of School = 5 km.
    ∴  Required time = 2
    5
    hours
    15/4

    =
    2 × 5 × 4
    hours
    15

    =
    8
    hours
    3

    =
    8
    × 60 minutes
    3

    = 160 minutes


  1. A car completed a journey of 400 km in 12
    1
    hrs.
    2
    The first
    3
    th of the journey was done at 30 km/hr.
    4
    Calculate the speed for the rest of the journey.
    1. 45 km/hr
    2. 25 km/hr
    3. 40 km/hr
    4. 30 km/hr

  1. View Hint View Answer Discuss in Forum

    Total distance covered = 400 km.

    Total time =
    25
    hours
    2

    ∴ 
    3
    th of total journey
    4

    =
    3
    × 400 = 300 km.
    4

    Time taken =
    Distance
    Speed

    =
    300
    = 10 hours
    30

    Remaining time =
    25
    − 2
    2

    =
    25 − 20
    =
    5
    hours
    22

    Remaining distance = 100 km.
    ∴  Required speed of car =
    100
    5
    2

    =
    100 × 2
    = 40 kmph.
    5

    Correct Option: C

    Total distance covered = 400 km.

    Total time =
    25
    hours
    2

    ∴ 
    3
    th of total journey
    4

    =
    3
    × 400 = 300 km.
    4

    Time taken =
    Distance
    Speed

    =
    300
    = 10 hours
    30

    Remaining time =
    25
    − 2
    2

    =
    25 − 20
    =
    5
    hours
    22

    Remaining distance = 100 km.
    ∴  Required speed of car =
    100
    5
    2

    =
    100 × 2
    = 40 kmph.
    5



  1. A man goes to a place on bicycle at speed of 16 km/hr and comes back at lower speed. If the average speed is 6.4 km/hr in total journey, then the return speed (in km/hr) is :
    1. 10
    2. 8
    3. 6
    4. 4

  1. View Hint View Answer Discuss in Forum

    Let the speed of cyclist while returning be x kmph.

    ∴  Average speed =
    2 × 16 × x
    16 + x

    ⇒  6.4 =
    32x
    16 + x

    ⇒  6.4 × 16 + 6.4x = 32x
    ⇒  32x – 6.4x = 6.4 × 16
    ⇒  25.6x = 6.4 × 16
    ⇒  x =
    6.4 × 16
    25.6

    = 4 kmph.

    Correct Option: D

    Let the speed of cyclist while returning be x kmph.

    ∴  Average speed =
    2 × 16 × x
    16 + x

    ⇒  6.4 =
    32x
    16 + x

    ⇒  6.4 × 16 + 6.4x = 32x
    ⇒  32x – 6.4x = 6.4 × 16
    ⇒  25.6x = 6.4 × 16
    ⇒  x =
    6.4 × 16
    25.6

    = 4 kmph.