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. 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. 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. 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. 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. 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