Speed, Time and Distance


  1. A car travels a distance of 300 kms at uniform speed. If the speed of the car is 5 km per hr more it takes two hours less to cover the same distance. Find the original speed of the car.
    1. 25 kmph
    2. 20 kmph
    3. 24 kmph
    4. 28 kmph

  1. View Hint View Answer Discuss in Forum

    Let the original speed of the car = x km per hr.
    When it is increased by 5 km
    per hr, the speed = x + 5 km per hr.
    As per the given information in the question,

    300
    300
    = 2
    xx + 5

    ⇒ 
    300(x + 5) − 300x
    = 2
    x(x + 5)

    ⇒ 
    300x + 1500 − 300x
    = 2
    x2 + 5x

    ⇒ 
    1500
    = 2
    x2 + 5x

    ⇒ 
    750
    = 2
    x2 + 5x

    ⇒  x2 + 5x = 750
    ⇒  x2 + 5x – 750 = 0
    ⇒  x2 + 30x – 25x – 750 = 0
    ⇒  x (x + 30) – 25 (x + 30) = 0
    ⇒  (x + 30) (x – 25) = 0
    ⇒  x = – 30 or 25
    The negative value of speed is inadmissible.
    Hence, the required speed = 25 km per hr.

    Correct Option: A

    Let the original speed of the car = x km per hr.
    When it is increased by 5 km
    per hr, the speed = x + 5 km per hr.
    As per the given information in the question,

    300
    300
    = 2
    xx + 5

    ⇒ 
    300(x + 5) − 300x
    = 2
    x(x + 5)

    ⇒ 
    300x + 1500 − 300x
    = 2
    x2 + 5x

    ⇒ 
    1500
    = 2
    x2 + 5x

    ⇒ 
    750
    = 2
    x2 + 5x

    ⇒  x2 + 5x = 750
    ⇒  x2 + 5x – 750 = 0
    ⇒  x2 + 30x – 25x – 750 = 0
    ⇒  x (x + 30) – 25 (x + 30) = 0
    ⇒  (x + 30) (x – 25) = 0
    ⇒  x = – 30 or 25
    The negative value of speed is inadmissible.
    Hence, the required speed = 25 km per hr.


  1. A boy walks from his house at 4 km per hr. and reaches his school 9 minutes late. If his
    speed had been 5 km per hr. he would have reached his school 6 minutes earlier. How far his school from house?
    1. 6.5 km.
    2. 5.5 km.
    3. 6 km.
    4. 5 km.

  1. View Hint View Answer Discuss in Forum

    Let time taken to reach school at 4 kmph be x hrs.
    Then time taken to reach school

    at 5 kmph = x +
    15
    hrs
    60

    Since, distance is equal.
    ∴   4x = 5 x +
    15
    60

    x =
    5
    hrs.
    4

    Hence, distance between school & house
    = 4 ×
    5
    km = 5 km
    4

    Correct Option: D

    Let time taken to reach school at 4 kmph be x hrs.
    Then time taken to reach school

    at 5 kmph = x +
    15
    hrs
    60

    Since, distance is equal.
    ∴   4x = 5 x +
    15
    60

    x =
    5
    hrs.
    4

    Hence, distance between school & house
    = 4 ×
    5
    km = 5 km
    4



  1. When a person covers the distance between his house and office at 50 km per hr. he is late by 20 minutes. But when he travels at 60 km per hr. he reaches 10 minutes early. What is the distance between his office and his house?
    1. 140 km.
    2. 160 km.
    3. 150 km.
    4. 120 km

  1. View Hint View Answer Discuss in Forum

    Let time taken to reach office at 50 kmph be x hrs
    Then time taken to reach office

    at 60 kmph = x +
    30
    hrs
    60

    As, distance covered is same,
    ∴  x × 50 = 60 x +
    30
    60

    50x = 60x + 30
    ⇒  x = 3 hrs
    Hence, distance = 3 × 50
    = 150 km

    Correct Option: C

    Let time taken to reach office at 50 kmph be x hrs
    Then time taken to reach office

    at 60 kmph = x +
    30
    hrs
    60

    As, distance covered is same,
    ∴  x × 50 = 60 x +
    30
    60

    50x = 60x + 30
    ⇒  x = 3 hrs
    Hence, distance = 3 × 50
    = 150 km


  1. A man covers one-third of his journey at 30 km per hr. and the remaining two-third at 45 km per hr. If the total journey is of 150 kms, what is his average speed for the whole journey?
    1. 38 kmph
    2. 38
      4
      kmph
      7
    3. 64 kmph
    4. 39
      4
      kmph
      7

  1. View Hint View Answer Discuss in Forum

    Length of journey = 150 kms

    1
    rd of journey =
    150
    = 50 kms
    33

    Remaining
    2
    journey
    3

    = 150 – 50 = 100 kms
    Time taken in
    1
    rd journey at 30 km per hr.
    3

    t1 =
    50
    =
    5
    hrs.
    303

    Time taken in
    2
    rd journey at 45 km per hr.
    3

    t2 =
    100
    =
    20
    hrs.
    459

    Total time taken in whole journey = t1 + t2
    =
    5
    +
    20
    =
    15 + 20
    =
    35
    hrs.
    3999

    Average Speed =
    150
    =
    150 × 9
    =
    270
    35/9357

    = 38
    4
    km per hr.
    7

    Correct Option: B

    Length of journey = 150 kms

    1
    rd of journey =
    150
    = 50 kms
    33

    Remaining
    2
    journey
    3

    = 150 – 50 = 100 kms
    Time taken in
    1
    rd journey at 30 km per hr.
    3

    t1 =
    50
    =
    5
    hrs.
    303

    Time taken in
    2
    rd journey at 45 km per hr.
    3

    t2 =
    100
    =
    20
    hrs.
    459

    Total time taken in whole journey = t1 + t2
    =
    5
    +
    20
    =
    15 + 20
    =
    35
    hrs.
    3999

    Average Speed =
    150
    =
    150 × 9
    =
    270
    35/9357

    = 38
    4
    km per hr.
    7



  1. An aeroplane travels a distance in the form of a square with the speed of 400 km per hr, 600 km per hr, 800 km per hr. and 1200 km per hr respectively. Find the average speed for the whole distance along the four sides of the square.
    1. 640 kmph
    2. 620 kmph
    3. 630 kmph
    4. 650 kmph

  1. View Hint View Answer Discuss in Forum

    As distance is covered along four sides (equal) of a square at different speeds, the average speed of the aeroplane

    =
    4
    1
    +
    1
    +
    1
    +
    1
    4006008001200

    [∵  All the sides of square are equal, so distance between them is same]
    =
    4
    30 + 20 + 15 + 10
    12000

    =
    48000
    = 640 km per hr.
    75

    Correct Option: A

    As distance is covered along four sides (equal) of a square at different speeds, the average speed of the aeroplane

    =
    4
    1
    +
    1
    +
    1
    +
    1
    4006008001200

    [∵  All the sides of square are equal, so distance between them is same]
    =
    4
    30 + 20 + 15 + 10
    12000

    =
    48000
    = 640 km per hr.
    75