Question 14

Explanation

Determining Time per Segment

Based on the previous track analysis, it is known that to pass checkpoint $C$ $3$ times, the runner covers a total of $10$ normal track segments in $12$ minutes. Thus, the travel time for one normal segment is:

Calculating Time for the New Path

We are asked to find the travel time from $A$ to $D$ given that the distance from $C$ to $D$ is widened to $2$ times the original length.

The normal route from $A$ to $D$ follows the path:

The breakdown of segments is:

1. $A \to B$: $1$ normal segment.
2. $B \to C$: $1$ normal segment.
3. $C \to D$: Since it is widened $2$ times, this is equivalent to $2$ normal segments.

The total effective segments to be covered is:

Thus, the total time required is:

Therefore, the time required for the runner to go from checkpoint $A$ to $D$ is $4.8$ minutes.