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:

$$\begin{gathered} s_1=5\cdot 15\mathrm{/}60=1.25km \\ {s}_J=5\cdot 1.5\mathrm{/}60=0.125km \\ {s}_O=(7\cdot 0.5+3\cdot 1)\mathrm{/}60=0.10833km \\ 0.10833km<0.125km \\ {s}_O<s_J=>t=\inf min \end{gathered}$$

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