Running Dogs
Two dogs start running around a 410 m circular track from the same point at the same time in opposite directions and with speeds in the ratio 7:9 . How far from the starting point do they meet for the seventh time?
The answer is 25.625.
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1 solution
[HINT]
Just go in the frame of any one dog and find the time of seventh meeting. Now as time remains same in any frame, come back in Earth's frame and check that how much distance any one of the dogs has traveled in that time (You can check this for any dog because both would be at same position, as it is their meeting time. Moreover, as both are at same position, their separation from initial position will also be same, which is the required answer). Subtract 410 from it as many times as you can, as we need only the separation from initial position.
Finally you get answer as 25.625 . I did it this way. Post your solution, if you have a better one.