Two cars on ring

There were two cars on the round track (ring) in the adjacent tracks, the first car on the inner track and the second on the outer track.
Both cars started at the same time from one starting track.
The first toy car drove four laps simultaneously, and the second toy car drove three.
The car did not change speed while driving.
a) Both cars started in the same direction. The second car drove the first 50 laps. Determine how often the first car caught up with him during this ride.
b) Both cars started in the same direction. The first car drove the first ten laps. Determine how many times the second car caught up during the ride.
c) The second car started opposite the first car. The second car drove the first five laps.
Determine how many times both cars passed during this ride - the first time both cars passed right after the start.

Correct answer:

a =  3
b =  0
c =  0

Step-by-step explanation:

$$\begin{gathered} 4s_1=4o \\ {s}_2=3o \\ v=s/t \\ {v}_1=4o/t \\ {v}_2=3o/t \\ 3v_1=4v_2 \\ {v}_1:v_2=4:3 \\ 4:3\dots 8:6\dots 10:7.5 \\ a=3 \end{gathered}$$

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