Question 13

Explanation

Track Analysis

The track is circular with $4$ checkpoints: $A, B, C, D$. A full lap consists of $4$ segments: $A \to B$, $B \to C$, $C \to D$, and $D \to A$. The journey starts from $A$.

Calculating Initial Distance

The runner passes checkpoint $C$ $3$ times.

• 1st time: $A \to B \to C$ ($2$ segments).
• 2nd time: Add 1 full lap ($4$ segments). Total: $2 + 4 = 6$ segments.
• 3rd time: Add 1 full lap ($4$ segments). Total: $6 + 4 = 10$ segments.

It is known that the travel time for $10$ segments is $12$ minutes. The time per segment ($t_s$) is:

Calculating Total Time

To reach checkpoint $C$ for the 4th time, the runner must cover 1 more lap ($4$ segments). The total segments covered are:

Thus, the total time required is:

Therefore, the time required by the runner is $16.8 \text{ minutes}$.