Speed, Time and Distance

Speed, Time and Distance

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Aptitude miscellaneous
  1. Two train of length 250 m and 140 m are running on parallel lines in the same direction at 58 km/h and 32 km/h, respectively. Find the time taken by the slower train to pass the driver of the faster one ?








  1. View Hint View Answer Discuss in Forum

    Relative speed = (58 - 32) = 26 km/h
    = 26 x (5/18) m/s = 65/9 m/s
    Time taken to cross each other = (250 + 140)/(65/9)

    Correct Option: B

    Relative speed = (58 - 32) = 26 km/h
    = (26 x 5/18) m/s = 65/9 m/s
    Time taken to cross each other = (250 + 140)/(65/9)
    = (390 x 9)/65 = 54 s

  1. A student goes to his school from his house walking at 4 km/h and reaches his school 10 min late. Next day, starting at the same time he walks as 6 km/h and reaches his school 5 min earlier than the scheduled time. Find the distance between school and home ?








  1. View Hint View Answer Discuss in Forum

    Let the distance be x km.
    ∴ Time = Distance/speed
    1st day time taken = x/4 h
    2nd day time taken = x/6 h
    Difference in time = (x/4 - x/6) h
    Actual difference between these two times = 15 min = 1/4 h
    ∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4

    Correct Option: B

    Let the distance be x km.
    ∴ Time = Distance/speed
    1st day time taken = x/4 h
    2nd day time taken = x/6 h
    Difference in time = (x/4 - x/6) h
    Actual difference between these two times = 15 min = 1/4 h
    ∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4
    ∴ x = 3 km

  1. An express train travelled at an average speed of 100 km/h, stopping for 3 min after every 75 km. A local train travelled at a speed of 50 km/h, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time in which the express train travel 600 km ?








  1. View Hint View Answer Discuss in Forum

    Time taken by express train to cover 75 km including stoppage
    = (60 / 100 x 75) min + = 48 min
    Time taken by express train to cover 600 km.
    = Time taken by it to cover 75 km
    = (48 / 75 x 525 ) min + (60 / 100 x 75 ) min
    = (336 + 45) min = 381
    Time taken by local train to9 cover 25 km including stoppage
    = (60 / 50 x 25) min + 1 min = 31 min
    In 31 min, distance covered = 25 km
    In(31 x 12) min. distance covered
    = (25 / 31 x 31 x 12 ) = 300 km
    In last 9 min, distance covered

    Correct Option: C

    Time taken by express train to cover 75 km including stoppage
    = (60 / 100 x 75) min + = 48 min
    Time taken by express train to cover 600 km.
    = Time taken by it to cover 75 km
    = (48 / 75 x 525 ) min + (60 / 100 x 75 ) min
    = (336 + 45) min = 381
    Time taken by local train to9 cover 25 km including stoppage
    = (60 / 50 x 25) min + 1 min = 31 min
    In 31 min, distance covered = 25 km
    In(31 x 12) min. distance covered
    = (25 / 31 x 31 x 12 ) = 300 km
    In last 9 min, distance covered
    = (25 / 31 x 9 ) = 7.25 km
    ∴ Required total distance
    = 300 + 7.25 = 307.25 km

  1. A car starts running with the initial speed of 40 km/h with its speed increasing every hour by 5 km/h. How many hours will it taken to cover a distance of 385 km ?








  1. View Hint View Answer Discuss in Forum

    Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
    Given, sum of the series is 385
    ∴ a = 40, d=5, s = 385 and n= ?
    Using S = n/2[2a + (n - 1)d]
    ⇒ 385 = n/2[80 + 5n - 5]

    Correct Option: D

    Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
    Given, sum of the series is 385
    ∴ a = 40, d=5, s = 385 and n= ?
    Using S = n/2[2a + (n - 1)d]
    ⇒ 385 = n/2[80 + 5n - 5]
    ⇒ 770 = 5n2 + 75n
    ⇒ n2 + 15n - 154 = 0
    ⇒ n2 + 22n - 7n - 154 = 0
    ⇒ n(n + 22) - 7(n + 22) = 0
    ⇒ (n + 22) (n - 7) = 0
    ∴ n = 7
    Remaining part = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 i.e., 1/30 th part is filled by B in 1 min
    Hence, required time to fill the whole tank = (165 + 1 + 1) min = 167 min

  1. Two cars A and B are running towards each other from two different place 88 km apart. If the ratio of the speeds of the cars A and B is 5:6 and the speeds of the cars B is 90 km/h, after what time will they meet each other ?








  1. View Hint View Answer Discuss in Forum

    Let speed of A = 5x
    Then, spend of B = 6x
    Given that,speed of B = 6x = 90
    ∴ x = 90/6 = 15
    ∴ Speed of A = 5x = 5x = 5 x 15 = 75 km/h
    Let A and B meet after T h. Then,
    75 x T + 90 x T =88

    Correct Option: D

    Let speed of A = 5x
    Then, spend of B = 6x
    Given that,speed of B = 6x = 90
    ∴ x = 90/6 = 15
    ∴ Speed of A = 5x = 5x = 5 x 15 = 75 km/h
    Let A and B meet after T h. Then,
    75 x T + 90 x T =88
    ∴ T = 88/165 h = (88 x 60)/165 = 32 min