Speed, Time and Distance


  1. A student goes to school at the
    rate of
    5
    km/hr and reaches 6 minutes late.
    2
    If he travels at the speed of 3 km/hr, he reaches 10 minutes earlier. The distance of the school is
    1. 45 km
    2. 20 km
    3. 10 km
    4. 4 km

  1. View Hint View Answer Discuss in Forum

    Distance of school = x km
    Difference of time

    = 16 minutes =
    16
    hour
    60

    ∴ 
    x
    x
    =
    16
    5/2360

    ⇒ 
    2x
    x
    =
    4
    5315

    ⇒ 
    6x − 5x
    =
    4
    1515

    ⇒ 
    x
    =
    4
    1515

    ⇒ x =
    4
    × 15 = 4km
    15


    Second Method :
    Here, S1 =
    5
    ,t1 = 6
    2

    S2 = 3, t2 = 10
    Distance =
    (S1 × S2)(t1 + t2)
    S1 − S2

    =
    5
    × 3(6 + 10)
    2
    3 -
    5
    2

    = 15 ×
    16
    km = 4 km.
    60

    Correct Option: D

    Distance of school = x km
    Difference of time

    = 16 minutes =
    16
    hour
    60

    ∴ 
    x
    x
    =
    16
    5/2360

    ⇒ 
    2x
    x
    =
    4
    5315

    ⇒ 
    6x − 5x
    =
    4
    1515

    ⇒ 
    x
    =
    4
    1515

    ⇒ x =
    4
    × 15 = 4km
    15


    Second Method :
    Here, S1 =
    5
    ,t1 = 6
    2

    S2 = 3, t2 = 10
    Distance =
    (S1 × S2)(t1 + t2)
    S1 − S2

    =
    5
    × 3(6 + 10)
    2
    3 -
    5
    2

    = 15 ×
    16
    km = 4 km.
    60


  1. A truck travels at 90 km/hr for
    the first 1
    1
    hours. After that it travels at 70 km/hr.
    2
    Find the time taken by the truck to travel 310 kilometres.
    1. 2.5 hrs
    2. 3 hrs
    3. 3.5 hrs
    4. 4 hrs

  1. View Hint View Answer Discuss in Forum

    Distance covered by truck in
    3
    hours
    2

    = Speed × Time
    = 90 ×
    3
    = 135 km
    2

    Remaining distance
    = 310 – 135 = 175 km
    ∴  Time taken at 70 kmph
    =
    175
    = 2.5 hours
    70

    ∴  Total time = 1.5 + 2.5 = 4 hours

    Correct Option: D

    Distance covered by truck in
    3
    hours
    2

    = Speed × Time
    = 90 ×
    3
    = 135 km
    2

    Remaining distance
    = 310 – 135 = 175 km
    ∴  Time taken at 70 kmph
    =
    175
    = 2.5 hours
    70

    ∴  Total time = 1.5 + 2.5 = 4 hours



  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. 20 minutes
    3. 30 minutes
    4. 1 hour

  1. View Hint View Answer Discuss in Forum

    Speed of B = x kmph (let)
    Speed of A = 2x kmph

    Speed of C =
    x
    kmph
    3

    ∴ 
    Speed of A
    =
    2x
    = 6
    Speed of C(x/3)

    ∴  Required time =
    1
    of
    3
    hours
    62

    =
    1
    hour = 15 minutes
    4

    Correct Option: A

    Speed of B = x kmph (let)
    Speed of A = 2x kmph

    Speed of C =
    x
    kmph
    3

    ∴ 
    Speed of A
    =
    2x
    = 6
    Speed of C(x/3)

    ∴  Required time =
    1
    of
    3
    hours
    62

    =
    1
    hour = 15 minutes
    4


  1. Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor-cyclist Q
    started from the same place but with a speed of 40 km/hr. How much time (in hours) will Q take to overtake P ?
    1. 1
    2. 3
      2
    3. 3
      8
    4. 2

  1. View Hint View Answer Discuss in Forum

    Distance covered by motor cyclist P in 30 minutes

    = 30 ×
    1
    = 15 km
    2

    Relative speed
    = 40 – 30 = 10 kmph
    ∴  Required speed = Time taken to cover is km at 10 kmph
    =
    15
    =
    3
    hour
    102

    Correct Option: B

    Distance covered by motor cyclist P in 30 minutes

    = 30 ×
    1
    = 15 km
    2

    Relative speed
    = 40 – 30 = 10 kmph
    ∴  Required speed = Time taken to cover is km at 10 kmph
    =
    15
    =
    3
    hour
    102



  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 is equal to
    1. 40 minutes
    2. 40
      minutes
      3
    3. 20 minutes
    4. 15 minutes

  1. View Hint View Answer Discuss in Forum

    Time = 12 minutes

    =
    12
    hour =
    1
    hour
    605



    Speed of train =
    10
    1
    5

    = 50 kmph
    New speed = 50 – 5 = 45 kmph
    ∴  Required time =
    Distance
    Speed

    =
    10
    =
    2
    hour
    459

    =
    2
    × 60 minutes
    9

    =
    40
    minutes
    3


    Second Method :
    Here, S1 =
    10
    km/min
    12

    =
    10
    × 60km/hr
    12

    = 50 km/hr, t1 =
    12
    =
    1
    hr
    605

    S2 = 45 km/hr, t2 = ?
    S1t1 = S2t2
    50 ×
    1
    = 45 × t2
    5
    t2 =
    10
    × 60 min
    45

    =
    40
    min
    3

    Correct Option: B

    Time = 12 minutes

    =
    12
    hour =
    1
    hour
    605



    Speed of train =
    10
    1
    5

    = 50 kmph
    New speed = 50 – 5 = 45 kmph
    ∴  Required time =
    Distance
    Speed

    =
    10
    =
    2
    hour
    459

    =
    2
    × 60 minutes
    9

    =
    40
    minutes
    3


    Second Method :
    Here, S1 =
    10
    km/min
    12

    =
    10
    × 60km/hr
    12

    = 50 km/hr, t1 =
    12
    =
    1
    hr
    605

    S2 = 45 km/hr, t2 = ?
    S1t1 = S2t2
    50 ×
    1
    = 45 × t2
    5
    t2 =
    10
    × 60 min
    45

    =
    40
    min
    3