Variable Speed Problem: Calculate Distance Covered at 34 km/h on 100m Track

To solve this problem, we'll determine the fraction of the track John covers at a speed of 34 km/h.

• Step 1: Understand that John runs three segments of the track:
  • 50 meters at 38 km/h
  • 25 meters at 36 km/h
  • 25 meters at 34 km/h
• Step 2: Identify that the question specifically asks about the third segment, which is 25 meters.
• Step 3: Calculate the fraction of the track these 25 meters represent out of 100 meters: $\text{Fraction at 34 km/h} = \frac{25 \text{ meters}}{100 \text{ meters}} = \frac{1}{4}$
• Step 4: The calculation shows that John covers $\frac{1}{4}$ of the track at a speed of 34 km/h.
• Step 5: Double-check by verifying the simplification and ensuring the calculation matches the track setup and speed descriptions.

Therefore, the solution to the problem is $\frac{1}{4}$.