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. 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. 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. 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. 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. 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