Speed, Time and Distance


  1. If a train runs at 70 km/hour, it reaches its destination late by 12 minutes. But if it runs at 80 km/ hour, it is late by 3 minutes. The correct time to cover the journey is









  1. View Hint View Answer Discuss in Forum

    Distance of journey = x km
    Difference of time = 12 – 3 = 9 minutes

    =
    9
    hour =
    3
    hour
    6020

    ∴  
    x
    x
    =
    3
    708020

    ⇒  
    x
    x
    =
    3
    782

    ⇒ 
    8x − 7x
    =
    3
    562

    ⇒ 
    x
    =
    3
    562

    ⇒  x =
    3
    × 56 = 84 km
    2

    ∴   Required correct time
    =
    84
    hours – 12 minutes
    70

    =
    84
    × 60 − 12 minutes
    70

    = 72 – 12 = 60 minutes
    = 1 hour

    Correct Option: C

    Distance of journey = x km
    Difference of time = 12 – 3 = 9 minutes

    =
    9
    hour =
    3
    hour
    6020

    ∴  
    x
    x
    =
    3
    708020

    ⇒  
    x
    x
    =
    3
    782

    ⇒ 
    8x − 7x
    =
    3
    562

    ⇒ 
    x
    =
    3
    562

    ⇒  x =
    3
    × 56 = 84 km
    2

    ∴   Required correct time
    =
    84
    hours – 12 minutes
    70

    =
    84
    × 60 − 12 minutes
    70

    = 72 – 12 = 60 minutes
    = 1 hour


  1. A train travelling at a speed of 55 km/hr travels from place X to place Y in 4 hours. If its speed is increased by 5 km/hr., then the time of journey is reduced by









  1. View Hint View Answer Discuss in Forum

    Distance between stations X and Y = Speed × Time
    = 55 × 4 = 220 km.
    New speed = 55 + 5 = 60 kmph

    ∴   Required time =
    220
    60

    =
    11
    hours
    3

    = 3 hours 40 minutes.
    ∴   Required answer
    = 4 hours – 3 hours 40 minutes
    = 20 minutes

    Correct Option: C

    Distance between stations X and Y = Speed × Time
    = 55 × 4 = 220 km.
    New speed = 55 + 5 = 60 kmph

    ∴   Required time =
    220
    60

    =
    11
    hours
    3

    = 3 hours 40 minutes.
    ∴   Required answer
    = 4 hours – 3 hours 40 minutes
    = 20 minutes



  1. If a boy walks from his house to school at the rate of 4 km per hour, he reaches the school 10 minutes earlier than the scheduled time. However, if he walks at the rate of 3 km per hour, he reaches 10 minutes late. Find the distance of his school from his house.









  1. View Hint View Answer Discuss in Forum

    Let the distance of school be x km, then

    x
    x
    =
    20
    3460

    ⇒ 
    x
    =
    1
    ⇒ x =
    12
    = 4 km
    1233


    Second Methdod :
    Here, S1 = 3, t1 = 10
    S2 = 4, t2 = 10
    Distance =
    (S1 ×S2)(t1 + t2)
    S2 −S1

    =
    (3 × 4)(10 + 10)
    4 − 3

    = 12 ×
    20
    = 4 km
    60

    Correct Option: B

    Let the distance of school be x km, then

    x
    x
    =
    20
    3460

    ⇒ 
    x
    =
    1
    ⇒ x =
    12
    = 4 km
    1233


    Second Methdod :
    Here, S1 = 3, t1 = 10
    S2 = 4, t2 = 10
    Distance =
    (S1 ×S2)(t1 + t2)
    S2 −S1

    =
    (3 × 4)(10 + 10)
    4 − 3

    = 12 ×
    20
    = 4 km
    60


  1. Walking at a speed of 5 km/hr, a man reaches his office 6 minutes late. Walking at 6 km/hr, he reaches there 2 minutes early. The distance of his office is









  1. View Hint View Answer Discuss in Forum

    Let the distance of the office be x km, then

    x
    x
    =
    8
    5660

    ⇒ 
    6x − 5x
    =
    2
    3015

    ⇒  x = 2 × 2 = 4 km

    Second Methdod :
    Here, S1 = 5, t1 = 6
    S2 = 6, t2 = 2
    Distance =
    (S1 ×S2)(t1 + t2)
    S2 −S1

    =
    (6 × 5)(6 + 2)
    6 − 5

    = 30 ×
    8
    = 4 km
    60

    Correct Option: B

    Let the distance of the office be x km, then

    x
    x
    =
    8
    5660

    ⇒ 
    6x − 5x
    =
    2
    3015

    ⇒  x = 2 × 2 = 4 km

    Second Methdod :
    Here, S1 = 5, t1 = 6
    S2 = 6, t2 = 2
    Distance =
    (S1 ×S2)(t1 + t2)
    S2 −S1

    =
    (6 × 5)(6 + 2)
    6 − 5

    = 30 ×
    8
    = 4 km
    60



  1. A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be :









  1. View Hint View Answer Discuss in Forum

    Speed of train =
    Distance
    Time

    =
    10
    kmph
    12
    60

    =
    10 × 60
    = 50 kmph
    12

    New speed = 45 kmph
    ∴   Required time =
    10
    hour
    45

    =
    2
    × 60 minutes
    9

    =
    40
    minutes
    3

    or 13 minutes 20 seconds

    Correct Option: B

    Speed of train =
    Distance
    Time

    =
    10
    kmph
    12
    60

    =
    10 × 60
    = 50 kmph
    12

    New speed = 45 kmph
    ∴   Required time =
    10
    hour
    45

    =
    2
    × 60 minutes
    9

    =
    40
    minutes
    3

    or 13 minutes 20 seconds