Time, Speed & Distance - Part 2 - Vikas Saini



  • A and B go by Bus from X to Z which is on the way to Y. C goes from Y to Z by Auto. A and B's Bus goes at 75km/hr and C's auto moves at 15 km/hr. All the three start at 6:00 am.B and A go ahead, meet C and pick him up. They return immediately to Z at the same time. The distance between X and Y is 600 km and XZ is 400 km.
    What is the total distance travelled by A ?
    What is time of entire journey ?

    Speed of A & B = 75 kmph.
    Speed of C = 15 kmph.
    Relative speed = 75+15 = 90kmph.
    Time they will meet = 600/90 = 6.66 = 6 hr 40 min.
    But after meeting with C, they pick up him and return to Z.
    At meeting point distance travelled by A & B = 75 x 6.66 = 500 km.
    Now Z is 100 km farther than this.
    Total distance travelled by A = 500+100 = 600 km. (Answer)
    Time of entire journey = 6.66 + 100/75 = 8 hr (Answer)

    When an object is dropped, the number of feet N that it falls is given by the formula N=(1/2)gt^2 where t is the time in seconds from the time it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

    In 5 seconds travelled by object = (1/2) x 32.2 x (5)^2.
    In first 3 seconds it travelled = (1/2) x 32.2 x (3)^2
    In last 2 seconds travelled = (1/2) x 32.2 x [5^2 – 3^2]
    = 16.1 x 16
    = 257.6

    In a 500 m race Dishu beats Ashu by 100 m or 5 seconds. In another race on the same track at the same speeds. Ashu and Prashant start at one end while Dishu starts at the opposite end. How many metres would Ashu have covered, by the time Dishu meets Prashant given that Dishu's speed is 10 m/sec more than that of Prashant.

    Speed ratio of Ashu & Dishu = 400 : 500 = 4:5.
    Ashu’s speed = 100/5 = 20 m/s.
    Dishu’s speed = 25 m/s.
    Prashant’s speed = 15m/s.
    Relative speed = 25+15 = 40 m/s.
    Time when Dishu and Prashant meet = 500 / 40 = 12.5 seconds.
    Distance travelled by Ashu in given time = 12.5 x 20 = 250 meter.

    Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has he been driving at 20 kmph?

    8 = D / 20 + (400 – D)/70
    8 = 7D + 800 – 2D / 140
    D = 64.
    Time = 64/20 = 3.2 = 3 hr 12 min.

    Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet?

    Let assume length of the train is ‘L’ and speed of train = a.
    Speed of man 1 = b.
    Speed of man 2 = c.
    20 = L / a – b.
    18 = L / a + c.
    18a + 18c = 20a – 20b.
    a = 10b + 9c.
    Distance of two men = 600 x (a + c).
    Time = 600(a+c) – 600(b+c) / (b+c)
    = 600 ( a – b) / (b + c)
    = 600 (10b + 10c – b) / (b + c)
    = 5400 seconds
    = 90 min (ans)

    Rohit and Virat walk from X and Y, a distance of 27 km at 5kmph and 7kmph respectively. Virat reaches Y and immediately turns back meeting Rohit at T. What is the distance of A to T ?

    Suppose T is p km away from Y.
    27 + p / 7 = 27 – p / 5
    5(27 + p) = 7 (27 – p)
    135 + 5p = 189 – 7p
    12p = 54.
    p = 4.5
    Distance from A = 27 – 4.5 = 22.5

    Donald and Trump leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Donald takes 4 hours to reach her destination, while Trump takes 9 hours to reach his destination. If the speed of Donald is 48 km/hr, what is the speed of Trump?

    Suppose speed of Donald is S1 and time is T1 after meeting each other.
    Speed of Trump is S2 and time T2 after meeting each other.
    After meeting, S1 / S2 = root (T2 / T1)
    48 / S2 = root (9 / 4)
    48 / S2 = 3 / 2
    S2 = 32.

    A, B and C start simultaneously from X to Y. A reaches Y, turns back and meet B at a distance of 11 km from Y. B reached Y, turns back and meet C at a distance of 9 km from Y. If the ratio of the speeds of A and C is 3:2, what is the distance between X and Y?

    Suppose distance between X and Y is D km.
    A = D+11, B = D-11.
    B = D+9, C = D-9.
    A/C = 3:2.
    (AB) / (BC) = 3/2.
    (D+11) (D+9) / (D-11) (D-9) = 3 / 2.
    D^2 + 20D + 99 / D^2 – 20D + 99 = 3 / 2
    2(D^2 + 20D + 99) = 3(D^2 – 20 D + 99)
    D^2 – 100 D + 99 = 0.
    D = 99.


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