Otto and Joachim

Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This keeps cycling. How long Otto Joachim catch up?

Correct result:

t =  -1 min

Solution:

$s_1 = 5\cdot 15/60 = 1.25 \ km \ \\ s_J = 5\cdot 1.5/60 = 0.125 \ km \ \\ s_O = (7\cdot 0.5 + 3\cdot 1)/60 = 0.10833 \ km \ \\ \ \\ 0.10833 \ km < 0.125 \ km \ \\ s_O < s_J => t=\inf \ min$

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