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. 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. 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. 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. 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. 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