Speed, Time and Distance


  1. Walking at
    3
    of his usual speed, a man reaches
    4
    his office 20 minutes late. Then his usual time for walking to his office is :
    1. 1 hour
    2. 30 minutes
    3. 45 minutes
    4. 40 minutes

  1. View Hint View Answer Discuss in Forum

    Usual time = x minutes

    New time =
    4x
    minutes
    3

    ∵  Speed ∝
    1
    Time

    According to the question,
    4x
    − x = 20
    3

    ⇒ 
    x
    = 20
    3

    ⇒  x = 60 minutes i.e. 1 hour.

    Correct Option: A

    Usual time = x minutes

    New time =
    4x
    minutes
    3

    ∵  Speed ∝
    1
    Time

    According to the question,
    4x
    − x = 20
    3

    ⇒ 
    x
    = 20
    3

    ⇒  x = 60 minutes i.e. 1 hour.


  1. Sarthak completed a marathon in 4 hours and 35 minutes. The marathon consisted of a 10 km run followed by 20 km cycle ride and the remaining distance again a run. He ran the first stage at 6 km/hr and then cycled at 16 km/hr. How much distance did Sarthak cover in total, if his speed in the last run was just half that of his first run?
    1. 5 km.
    2. 35 km.
    3. 40 km.
    4. 45 km.

  1. View Hint View Answer Discuss in Forum

    Let the total distance be x km.

    Time =
    Distance
    Speed

    According to the question,
    10
    +
    20
    +
    x − 30
    = 4
    35
    616360

    = 4
    7
    12

    ⇒  
    5
    +
    5
    +
    x
    − 10 =
    55
    34312

    ⇒  
    x
    +
    5
    +
    5
    − 10 =
    55
    33412

    ⇒ 
    x
    +
    20 + 15 − 120
    =
    55
    31212

    ⇒ 
    x
    85
    =
    55
    31212

    ⇒ 
    x
    =
    85
    +
    55
    =
    140
    3121212

    ⇒ x =
    140
    × 3 = 35 km.
    12

    Correct Option: B

    Let the total distance be x km.

    Time =
    Distance
    Speed

    According to the question,
    10
    +
    20
    +
    x − 30
    = 4
    35
    616360

    = 4
    7
    12

    ⇒  
    5
    +
    5
    +
    x
    − 10 =
    55
    34312

    ⇒  
    x
    +
    5
    +
    5
    − 10 =
    55
    33412

    ⇒ 
    x
    +
    20 + 15 − 120
    =
    55
    31212

    ⇒ 
    x
    85
    =
    55
    31212

    ⇒ 
    x
    =
    85
    +
    55
    =
    140
    3121212

    ⇒ x =
    140
    × 3 = 35 km.
    12



  1. Walking at the rate of 4 kmph a man covers certain distance in 2 hrs 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in how many minutes ?
    1. 50 min.
    2. 35 min.
    3. 40 min.
    4. 45 min.

  1. View Hint View Answer Discuss in Forum

    2 hours 45 minutes

    =2 +
    45
    hours
    60

    =2 +
    3
    hours
    4

    =
    11
    hours
    4

    ∴  Distance = Speed × Time
    = 4 ×
    11
    = 11 km.
    4

    ∴  Time taken in covering 11 km at 16.5 kmph
    =
    11
    hour
    16.5

    =
    11 × 10 × 60
    minutes
    165

    = 40 minutes

    Correct Option: C

    2 hours 45 minutes

    =2 +
    45
    hours
    60

    =2 +
    3
    hours
    4

    =
    11
    hours
    4

    ∴  Distance = Speed × Time
    = 4 ×
    11
    = 11 km.
    4

    ∴  Time taken in covering 11 km at 16.5 kmph
    =
    11
    hour
    16.5

    =
    11 × 10 × 60
    minutes
    165

    = 40 minutes


  1. A is twice as fast as B, and B is thrice as fast as C is. The journey covered by
    C in 1
    1
    hours will be covered by A in
    2
    1. 15 minutes
    2. 30 minutes
    3. 1 hour
    4. 10 minutes

  1. View Hint View Answer Discuss in Forum

    Time taken by C = t hours

    ∴   Time taken by B =
    t
    hours
    3

    and time taken by A =
    t
    hours
    6

    Here, t =
    3
    hours
    2

    ∴  Required time taken by A =
    3
    hour
    2
    6

    =
    1
    hour
    4

    =
    1
    × 60 minutes
    4

    = 15 minutes

    Correct Option: A

    Time taken by C = t hours

    ∴   Time taken by B =
    t
    hours
    3

    and time taken by A =
    t
    hours
    6

    Here, t =
    3
    hours
    2

    ∴  Required time taken by A =
    3
    hour
    2
    6

    =
    1
    hour
    4

    =
    1
    × 60 minutes
    4

    = 15 minutes



  1. A jeep is chasing a car which is 5km ahead. Their respective speed are 90 km/hr and 75 km/hr. After how many minutes will the jeep catch the car ?
    1. 18 min.
    2. 20 min.
    3. 24 min.
    4. 25 min.

  1. View Hint View Answer Discuss in Forum

    Relative speed
    = 95 – 75 = 15 kmph

    Required time =
    Distance
    Relative speed

    =
    5
    hours
    15

    =
    5
    × 60 minutes
    15

    = 20 minutes

    Correct Option: B

    Relative speed
    = 95 – 75 = 15 kmph

    Required time =
    Distance
    Relative speed

    =
    5
    hours
    15

    =
    5
    × 60 minutes
    15

    = 20 minutes