I came across this little riddle:
An amateur runner trains on a 1 250 m long track at a speed of $v_L = 2 m/s$. His dog runs ahead to the target, turns around and then runs back to him, then he runs back to the target, back, etc. His speed is when running forth $v_H = 5 m/s$ and when running back (because of the headwind) $v_Z = 4 m/s$. Calculate the distance traveled by the dog.
It is little bit like Zeno's paradoxes but with the additional complication that here the dog is running back and forth at different speeds.
Could anyone please give some hints how to elegantly tackle the problem or references where a solution can be found (Perhaps this riddle even has a common name under which it can be found in the literature)? Thank you!