Speed, Time and Distance


  1. A man walks a distance of 35 kms. He walks for some time at 4 km per hour and for some time at 5 km per hr. If he walks at 5 km per hr. instead of 4 km per hr. and 4 km per hr. instead of 5 km per hr, he will walk 2 kms more in the same span of time. Find his total time of total journey.
    1. 8.5 hours
    2. 7.5 hours
    3. 8 hours
    4. 7 hours

  1. View Hint View Answer Discuss in Forum

    Let the man walks for x hours at 4 km per hr. and y hours at 5 km per hr. and covers a distance of 35 kms.
    ∴  Distance = 4x + 5y = 35 ...(i)
    Now, he walks at 5 km per hr.
    for x hours and at 4 km per hr.
    for y hours and covers a distance (35 + 2) = 37 kms
    ∴  Distance = 5x + 4y = 37...(ii)
    By 5 × (i) – 4 × (ii) we have

    20x + 25y = 175
    20x + 16y = 148
        -       -       -
    ____________
            9y = 27

    ⇒  y = 3
    Putting the value of (y) in equation (i), we have
    4x + 5 × 3 = 35
    ⇒  4x = 35 – 15 = 20
    ⇒  x = 5
    ∴  Total time taken
    = x + y = 5 + 3 = 8 hours.

    Correct Option: C

    Let the man walks for x hours at 4 km per hr. and y hours at 5 km per hr. and covers a distance of 35 kms.
    ∴  Distance = 4x + 5y = 35 ...(i)
    Now, he walks at 5 km per hr.
    for x hours and at 4 km per hr.
    for y hours and covers a distance (35 + 2) = 37 kms
    ∴  Distance = 5x + 4y = 37...(ii)
    By 5 × (i) – 4 × (ii) we have

    20x + 25y = 175
    20x + 16y = 148
        -       -       -
    ____________
            9y = 27

    ⇒  y = 3
    Putting the value of (y) in equation (i), we have
    4x + 5 × 3 = 35
    ⇒  4x = 35 – 15 = 20
    ⇒  x = 5
    ∴  Total time taken
    = x + y = 5 + 3 = 8 hours.


  1. Ram travelled one-third of a journey with a speed of 10 km per hr, the next one-third with a speed of 9 km per hr. and the rest at a speed of 8 km per hr. If he had travelled half the journey at speed of 10 km per hr. and the other half with a speed of 8 km per hr, he would have been 1 minute longer on the way. What distance did he travel?
    1. 36 km
    2. 32 km
    3. 35 km
    4. 40 km

  1. View Hint View Answer Discuss in Forum

    Let the total distance travelled be x kms.
    Case I :
    Speed for the first one-third distance

    i.e.
    x
    kms =10 km per hr.
    3

    ∴  Time taken =
    x
    hours
    30

    Similarly, time taken for the next one-third distance
    =
    x
    hours
    27

    and time taken for the last onethird distance
    =
    x
    hours.
    24

    ∴  Total time taken to cover x kms.
    =
    x
    +
    x
    +
    x
    hours.
    302724


    Case II :
    Time taken for one-half distance at the speed of 10 km per hr.
    =
    x
    hrs.
    20

    and time taken for remaining 1/2 of distance
    =
    x
    hrs. at 8 km per hr.
    16

    Total time taken =
    x
    +
    x
    hrs.
    2016

    Time taken in (Case II – Case I)
    = 1 minute =
    1
    hr.
    60

    ∴  According to the question
    x
    +
    x
    x
    +
    x
    +
    x
    2016302724

    =
    1
    60

    ⇒ 
    108x + 135x − 72x − 80x − 90x
    2160

    =
    1
    60

    ⇒ 
    243x − 242x
    =
    1
    216060

    ⇒ 
    x
    =
    1
    216060

    ⇒  x =
    2160
    = 36 km.
    60

    Hence the required distance
    = 36 km.

    Correct Option: A

    Let the total distance travelled be x kms.
    Case I :
    Speed for the first one-third distance

    i.e.
    x
    kms =10 km per hr.
    3

    ∴  Time taken =
    x
    hours
    30

    Similarly, time taken for the next one-third distance
    =
    x
    hours
    27

    and time taken for the last onethird distance
    =
    x
    hours.
    24

    ∴  Total time taken to cover x kms.
    =
    x
    +
    x
    +
    x
    hours.
    302724


    Case II :
    Time taken for one-half distance at the speed of 10 km per hr.
    =
    x
    hrs.
    20

    and time taken for remaining 1/2 of distance
    =
    x
    hrs. at 8 km per hr.
    16

    Total time taken =
    x
    +
    x
    hrs.
    2016

    Time taken in (Case II – Case I)
    = 1 minute =
    1
    hr.
    60

    ∴  According to the question
    x
    +
    x
    x
    +
    x
    +
    x
    2016302724

    =
    1
    60

    ⇒ 
    108x + 135x − 72x − 80x − 90x
    2160

    =
    1
    60

    ⇒ 
    243x − 242x
    =
    1
    216060

    ⇒ 
    x
    =
    1
    216060

    ⇒  x =
    2160
    = 36 km.
    60

    Hence the required distance
    = 36 km.



  1. Two men A and B start walking simultaneously from P to Q, a distance of 21 kms, at the speed of 3 km and 4 km an hour respectively. B reaches Q, returns immediately and meets A at R. Find the distance from P to R.
    1. 22 km
    2. 20 km
    3. 16 km
    4. 18 km

  1. View Hint View Answer Discuss in Forum

    Let A and B meet after time t hours.

    Distance covered by A in t hours = 3 t km.
    Distance covered by B in t hours = 4 t km.
    Total distance covered by A and B = (3t + 4t) km = 7 t km.
    From the diagram we can see that the total distance covered by A and B is equal to twice the distance between P and Q.
    ∴  7t = 2 × 21

    t =
    2 × 21
    = 6 hours
    2

    Distance PR = 6 × 3 = 18 km.

    Correct Option: D

    Let A and B meet after time t hours.

    Distance covered by A in t hours = 3 t km.
    Distance covered by B in t hours = 4 t km.
    Total distance covered by A and B = (3t + 4t) km = 7 t km.
    From the diagram we can see that the total distance covered by A and B is equal to twice the distance between P and Q.
    ∴  7t = 2 × 21

    t =
    2 × 21
    = 6 hours
    2

    Distance PR = 6 × 3 = 18 km.


  1. Two men A and B walk from X to Y a distance of 42 kms at 5 km and 7 km an hour respectively. B reaches Y and returns immediately and meets A at R. Find the distance from X to R.
    1. 32 km
    2. 30 km
    3. 35 km
    4. 40 km

  1. View Hint View Answer Discuss in Forum

    When B meets A at R, by then B has walked a distance (XY + YR) and A, the distance XR.
    That is both of them have together walked twice the distance from X to Y, i.e., 42 kms.

    Now, the ratio of speed of A and B is 5 : 7 and they walk 84 kms.
    ∴  Hence, the distance XR travelled by

    A =
    5
    × 84 = 35 kms.
    5 + 7

    Correct Option: C

    When B meets A at R, by then B has walked a distance (XY + YR) and A, the distance XR.
    That is both of them have together walked twice the distance from X to Y, i.e., 42 kms.

    Now, the ratio of speed of A and B is 5 : 7 and they walk 84 kms.
    ∴  Hence, the distance XR travelled by

    A =
    5
    × 84 = 35 kms.
    5 + 7



  1. Walking at
    3
    of his usual speed a man is late by
    4
    2
    1
    hours. The usual time would have been what?
    2
    1. 7 hours
    2. 7.5 hours
    3. 8 hours
    4. 8.5 hours

  1. View Hint View Answer Discuss in Forum

    New speed is
    3
    of the usual speed
    4

    ∴  New time taken =
    4
    of the usual time
    3

    ∴ 
    4
    of the usual time – Usual time =
    5
    32

    ⇒ 
    1
    of the usual time =
    5
    32

    ∴ Usual time =
    5
    × 3
    2

    =
    15
    hours or 7.5 hrs
    2

    Correct Option: B

    New speed is
    3
    of the usual speed
    4

    ∴  New time taken =
    4
    of the usual time
    3

    ∴ 
    4
    of the usual time – Usual time =
    5
    32

    ⇒ 
    1
    of the usual time =
    5
    32

    ∴ Usual time =
    5
    × 3
    2

    =
    15
    hours or 7.5 hrs
    2