School-Safe Puzzle Games

Speed and Distance Puzzle, Track Race

speed and distance puzzle man and dog

A man and his dog are racing on a circular track at constant speed. John can run once around the track in six minutes, and Ben (his Dog)  in four minutes. In how many minutes will Ben overtake John?

16 Comments to “Speed and Distance Puzzle, Track Race”


  1. o.najaee | Profile

    2.4 min :D
    funny


  2. Shawn | PUZZLE GRANDMASTER | Profile

    12 minutes


  3. suineg | PUZZLE MASTER | Profile

    Ok, I think it can be solved this way: (hope that there is circular velocity here)
    Assuming that both of them start at the same point and at the same moment, the dog overtake him, in time 0….01 cause he passed him, the dog velocity is greater than the man velocity, but I asumme that this mean when the dog meet again with his master.. so:
    In an easy way:
    John covers 1/3 of the lap distance in 2 minutes
    Ben covers 1/2 of the lap distance in 2 minutes
    1/2-1/3= 1/6 (distance that Ben gains over John every 2 min)
    six time this time… Ben would have gained exactly 1 lap
    that happen 6X2= 12 min… Ben meets John in 12 min so:
    Ben would overtake John in 12 min and 1 nanosecond… jajaja, cool


  4. Bobo The Bear | PUZZLE MASTER | Profile

    (Assuming they both start at the same point on the track …;)


    After 12 minutes, John will have done 2 laps, and his dog will have done 3 laps and will then overtake him.


  5. Bobo The Bear | PUZZLE MASTER | Profile

    One question: If John is running around the track, and the puzzle title says that it’s a bike race, does that mean that his dog is the one on the bicycle??


  6. RK | Founder | Profile

    Oops! title changed Bobo :)


  7. Hex | PUZZLE MASTER | Profile

    In 12 minutes, John would have made 2 laps and Ben 3.


  8. munna | Profile

    Assuming they John and Ben start from same point, Ben will overtake John in 12 minutes.


  9. Falwan | Profile

    x = time in hrs.


    D = diameter


    (xD/4) – (xD/6) = D


    (x/4) – (x/6) = 1


    3x – 2x = 12


    x = 12


    Mr. Ben will overtake Mr. John after 12 hrs.


  10. Falwan | Profile

    I considered the time in hours.


    So 12 min. in that case.


  11. RK | Founder | Profile

    Very good, 12 min is correct :)


  12. Hendy | Profile

    J = 1/6 rpm (1 revolution/ 6 minutes)
    B = 1/4 rpm (1 revolution/ 4 minutes)

    rJ = t * 1/6 rpm
    rB = t * 1/4 rpm

    rJ = x min * 1/6 r/min
    rB = x min * 1/4 r/min

    rJ = x * 1/6 r = x * 1/6 r
    rB = x* 1/4 r = x * 1/4 r

    rB = rJ + 1
    x * 1/4 r = x * 1/6 r + 1 r
    1/4-1/6 = 1/12
    1 r = x * 1/12 r
    1 = x * 1/12
    x = 12

    12 * 1/6 = 2
    12 * 1/4 = 3


    Overtaken in 12 laps (revolutions).


  13. Hendy | Profile

    Oops! That should be time in minutes, not revolutions. Not paying attention!


  14. Hedaiet El-Sabbahy | Profile

    *Assume that the speed of the man is (Sm = 1/6 RPM)and speed of Dog is (Sd=1/4 RPM)
    *Assume that they will meet again after (X) mins.
    * Then the No. of rounds covered by Man = 1/6 X, and by the Dog = 1/4 X.
    * As they will meet again, Then: (1/4 X = 1/6 X + 1).
    * Then: (1/4-1/6) X = 1 ==> (1/12) X = 1 ==> X = 12 Mins.
    THANKS FOR ALL


  15. Tsopi | Profile

    we must find at witch time man will have done x laps and dog x+1 laps
    H 1 lap – 6 minutes/D 1 lap – 4 minutes
    H 2 lap – 12 minutes/D 2 lap – 8 minutes
    H 3 lap – 18 minutes/D 3 lap – 12 minutes


    As we see at the time of 12 minutes the Human (H) has done 2 laps(x = 2) and the Dog(D) has made 3 (x + 1 = 2 + 1 = 3).
    Answer is 12


  16. venkatg70 | Profile

    Let a,b be the time taken by the person and dog respectively.


    Let a>b
    Let x be the time when they meet
    Then,


    x/a = fraction of the circular track covered by person
    x/b = fraction of the circular track covered by dog


    As they both run, gap created between them. When the gap (fraction of the track length)
    approaches “n” where n = 1,2,3…, they meet.


    For initial meet n =1, so


    So x/b – x/a = 1


    Solving, we get x = ab/(a-b)


    For eg: when a=6 min, b=4 min, x = 12 min


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