MATH CATCH-UP PROBLEM №1 (robot)

A robot starts chasing Vova. The robot moves at a constant speed of 5 km/h. Vova’s pace changes over time:

First 10 minutes: runs at 15 km/h
Next 10 minutes: walks at 3 km/h (to rest)
Next 10 minutes: runs at 10 km/h
Then: walks at 3 km/h
After that: runs at 8 km/h
Then: walks at 3 km/h

From that point onward, Vova repeats this cycle indefinitely: 10 minutes running at 6 km/h, then 10 minutes walking at 3 km/h.

When will the robot catch up to Vova?

First hour — 10-minute chunks (distance): Second hour — 30 minutes at 6 km/h, then 30 minutes at 3 km/h: Relative speed in cyclic phase and total time:

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