Speed, Time and Distance

Speed, Time and Distance

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  1. A man goes to the fair in Funcity with his son and faithful dog. Unfortunately man misses his son which he realises 20 minutes later. The son comes back towards his home at the speed of 20 m/min and man follows him at 40 m/min. The dog runs to the son (child) and comes back to the man (father) to show him the direction of his son. It keeps moving to and fro at 60 m/min between son and father, till the man meets the son. what is the distance travelled by the dog in the direction of the son?








  1. View Hint View Answer Discuss in Forum

    In 20 minutes the difference between man and his son = 20 x 20 = 400 m
    Distance travelled by dog when he goes towards son = (400/40) x 60 = 600 m and time required is 10 minutes
    In 10 minutes the remaining difference between man and son = 400 - (20 x 10) = 200 m

    Note: Relative speed of dog with child is 40 km/h and the same with man is 100 km/h.
    Time taken by dog to meet the man = 200/100 = 2 min
    In 2 minute the remaining distance between child and man = 200 - ( 2 x 20) = 160 m
    Now, the time taken by dog to meet the child again = 160/40 = 4 min
    In 4 minutes he covers 4 x 60 = 240 m distance while going towards the son.
    In 4 minute the remaining distance between man and child = 160 - (4 x 20) = 80 m
    Time required by dog to meet man once again = 80/100 = 0.8 min
    In 0.8 min remaining distance between man and child = 80 - (0.8 x 20) = 64 min
    Now, time taken by dog to meet the child again = (64/40) x (8/5) min
    ∴ Distance travelled by dog = (8/5) x 60 = 96 m
    Thus, we can observe that every next time dog just go 2/5th of previous distance to meet the child in the direction of child.

    Correct Option: D

    In 20 minutes the difference between man and his son = 20 x 20 = 400 m
    Distance travelled by dog when he goes towards son = (400/40) x 60 = 600 m and time required is 10 minutes
    In 10 minutes the remaining difference between man and son = 400 - (20 x 10) = 200 m

    Note: Relative speed of dog with child is 40 km/h and the same with man is 100 km/h.
    Time taken by dog to meet the man = 200/100 = 2 min
    In 2 minute the remaining distance between child and man = 200 - ( 2 x 20) = 160 m
    Now, the time taken by dog to meet the child again = 160/40 = 4 min
    In 4 minutes he covers 4 x 60 = 240 m distance while going towards the son.
    In 4 minute the remaining distance between man and child = 160 - (4 x 20) = 80 m
    Time required by dog to meet man once again = 80/100 = 0.8 min
    In 0.8 min remaining distance between man and child = 80 - (0.8 x 20) = 64 min
    Now, time taken by dog to meet the child again = (64/40) x (8/5) min
    ∴ Distance travelled by dog = (8/5) x 60 = 96 m
    Thus, we can observe that every next time dog just go 2/5th of previous distance to meet the child in the direction of child.
    So, we can calculate the total distance covered by dog in the direction of child with the help of GP formula.
    Here, first term (a) = 600 and common ratio (r) = 2/5
    Sum of the infinite GP = a/(1 - r)
    = 600/(1 - 2/5) = (600 x 5)/3 = 1000 m

  1. A hunter fired two shots from the branch of a tree at an interval of 76 seconds. A tiger separating too fast hears the two shots at an interval of 83 seconds. If the velocity of the sound is 1195.2 km/h, then find the speed of tiger?








  1. View Hint View Answer Discuss in Forum

    In case of increasing gap between two objects.
    Speed of sound / speed of tiger = Time utilised / Difference in time

    Correct Option: B

    In case of increasing gap between two objects.
    Speed of sound / speed of tiger = Time utilised / Difference in time
    ⇒ 1195.2 / x = 83 / 7
    x = 100.8 km/h

  1. A soldier fired two bullets at an interval of 335 seconds moving at a uniform speed v1. A terrorist who was running ahead of the soldier in the same direction, hears the two shots at an interval of 330 seconds? If the speed of sound is 1188 km/h, then who is the faster and by how much?








  1. View Hint View Answer Discuss in Forum

    Speed of wind (sound) / Relative speed of soldier and terrorist = Time utilised / Difference in time

    Correct Option: C

    Speed of wind (sound) / Relative speed of soldier and terrorist = Time utilised / Difference in time
    1188/x = 330/5
    x = 18 km/h and solder is faster.

  1. In reaching the Purnagiri a man took half as long again to climb the second third as he did to climb the first third and a quarter as long again for the last third as for the second third. He took altogether 5 hr 50 minutes. Find the time he spent on the first third of the journey?








  1. View Hint View Answer Discuss in Forum

    Let the time taken in first third part of the journey be x minutes, then the time required in second third part of the journey is 3x/2 and in the last third part of the journey time required is 15x/8.
    Therefore, x + (3x/2) + (15x/8) = 350min

    Correct Option: B

    Let the time taken in first third part of the journey be x minutes, then the time required in second third part of the journey is 3x/2 and in the last third part of the journey time required is 15x/8.
    Therefore, x + (3x/2) + (15x/8) = 350min
    ⇒ x = 80 min

  1. A man travels the first part of his journey at 20 km/h and the next at 70 km/h, covering the entire journey at an average speed of 50 km/h. What is the ratio of the distance that he covered at 20 km/h to that he covered at 70 km/h?








  1. View Hint View Answer Discuss in Forum

    x/20 + y/70 = (x + y)/50

    Correct Option: A

    x/20 + y/70 = (x + y)/50
    ⇒ (70x + 20y)/1400 = (x + y)/50
    ⇒ 42x = 8y
    ⇒ x/y = 4/21