Speed, Time and Distance


  1. A man walked a certain distance. One-third he walked at 5 km per hr. Another one-third he walked at 10 km per hr. and the rest at 15 km per hr. Find his average speed.
    1. 8
      1
      kmph
      11
    2. 7
      1
      kmph
      11
    3. 7
      2
      kmph
      11
    4. 8
      2
      kmph
      11

  1. View Hint View Answer Discuss in Forum

    Here, the man covers equal distance at different speeds. Using the formula, the Average Speed is given by

    =
    3
    1
    +
    1
    +
    1
    51015

    =
    3
    6 + 3 + 2
    30

    =
    90
    = 8
    2
    km per hour.
    1111

    Correct Option: D

    Here, the man covers equal distance at different speeds. Using the formula, the Average Speed is given by

    =
    3
    1
    +
    1
    +
    1
    51015

    =
    3
    6 + 3 + 2
    30

    =
    90
    = 8
    2
    km per hour.
    1111


  1. P and Q are two cities. A boy travels on cycle from P to Q at a speed of 20 km per hr. and returns at the rate of 10 km per hr. Find his average speed for the whole journey.
    1. 13
      2
      kmph
      3
    2. 12
      1
      kmph
      3
    3. 13
      1
      kmph
      3
    4. 12
      2
      kmph
      3

  1. View Hint View Answer Discuss in Forum

    Let the speed between P and Q be x km.

    Then time taken to cover x km. P to Q =
    x
    hrs.
    20

    Time taken to cover x km from Q to P at 10 km per hr. P to Q
    =
    x
    hrs.
    10

    ∴  Total distance covered
    = x + x = 2x km.
    Time taken to cover 2x km.
    =
    x
    +
    x
    =
    x + 2x
    =
    3x
    hrs.
    20102020

    ∴ Average Speed =
    2x
    =
    2x × 20
    3x/203x

    =
    40
    km per hr.
    3

    = 13
    1
    km per hr.
    3


    Second Method : Here, x = 20 km per hr.
    y = 10 km per hr
    ∴ Average Speed [∵  Distance is same]
    =
    2xy
    =
    2 × 20 × 10
    x + y20 + 10

    =
    400
    =
    40
    = 13
    1
    km per hr.
    3033

    Correct Option: C

    Let the speed between P and Q be x km.

    Then time taken to cover x km. P to Q =
    x
    hrs.
    20

    Time taken to cover x km from Q to P at 10 km per hr. P to Q
    =
    x
    hrs.
    10

    ∴  Total distance covered
    = x + x = 2x km.
    Time taken to cover 2x km.
    =
    x
    +
    x
    =
    x + 2x
    =
    3x
    hrs.
    20102020

    ∴ Average Speed =
    2x
    =
    2x × 20
    3x/203x

    =
    40
    km per hr.
    3

    = 13
    1
    km per hr.
    3


    Second Method : Here, x = 20 km per hr.
    y = 10 km per hr
    ∴ Average Speed [∵  Distance is same]
    =
    2xy
    =
    2 × 20 × 10
    x + y20 + 10

    =
    400
    =
    40
    = 13
    1
    km per hr.
    3033



  1. A person covers 10 kms at 4 km per hr. and then further 21 kms at 6 km per hr. Find his average speed for whole journey.
    1. 5
      1
      kmph
      3
    2. 5
      1
      kmph
      6
    3. 5
      1
      kmph
      2
    4. 4
      1
      kmph
      2

  1. View Hint View Answer Discuss in Forum

    Case I.
    Distance = 10 kms
    Speed = 4 km/hr.

    ∴  Time taken (t2) =
    21
    =
    7
    hrs.
    62

    Total time taken =
    5
    +
    7
    22

    =
    5 + 7
    = 6 hrs.
    2

    Total distance covered
    = 10 + 21 = 31 kms
    ∴   Average Speed =
    Total distance
    Total time

    =
    31
    km per hr.
    6

    = 5
    1
    km per hr.
    6

    Correct Option: B

    Case I.
    Distance = 10 kms
    Speed = 4 km/hr.

    ∴  Time taken (t2) =
    21
    =
    7
    hrs.
    62

    Total time taken =
    5
    +
    7
    22

    =
    5 + 7
    = 6 hrs.
    2

    Total distance covered
    = 10 + 21 = 31 kms
    ∴   Average Speed =
    Total distance
    Total time

    =
    31
    km per hr.
    6

    = 5
    1
    km per hr.
    6


  1. Walking at a speed of 6 km per hour, a man takes 5 hours to complete his journey. How much time will he need to complete the same journey at the rate of 8 km per hr.?
    1. 3
      3
      hours
      4
    2. 3 hours
    3. 2
      3
      hours
      4
    4. 3.5 hours

  1. View Hint View Answer Discuss in Forum

    Speed = 6 km/hr
    Time taken = 5 hours
    ∴  Distance covered
    = 6 × 5 = 30 kms
    ∴  Time required to cover 30 kms
    at the speed of 8 km/hr.

    =
    Distance
    =
    30
    =
    15
    hours
    Speed84

    = 3
    3
    hours
    4

    Correct Option: A

    Speed = 6 km/hr
    Time taken = 5 hours
    ∴  Distance covered
    = 6 × 5 = 30 kms
    ∴  Time required to cover 30 kms
    at the speed of 8 km/hr.

    =
    Distance
    =
    30
    =
    15
    hours
    Speed84

    = 3
    3
    hours
    4



  1. A car runs at 60 km per hr. A man runs at one-third the speed of the car and reaches office from his house in 15 minutes. How far is his office from his house?
    1. 7 km
    2. 5.5 km
    3. 6 km
    4. 5 km

  1. View Hint View Answer Discuss in Forum

    Man’s speed =
    1
    of the speed of car
    3
    =
    1
    × 60 = 20 km per hr.
    3

    Time taken to reach office= 15
    minutes =
    15
    =
    1
    hr.
    604

    ∴  Distance between his house and office
    = Speed × Time
    = 20 ×
    1
    = 5 km.
    4

    Correct Option: D

    Man’s speed =
    1
    of the speed of car
    3
    =
    1
    × 60 = 20 km per hr.
    3

    Time taken to reach office= 15
    minutes =
    15
    =
    1
    hr.
    604

    ∴  Distance between his house and office
    = Speed × Time
    = 20 ×
    1
    = 5 km.
    4