Step 1: Conceptual Understanding:
The statement "Ajay defeats Vijay by X meters" signifies that upon Ajay completing the race, Vijay is X meters behind the finish line. To determine this deficit, one must calculate Vijay's traveled distance during the time Ajay took to finish.
Step 2: Methodology:
1. Ascertain the speed of the slower participant (Vijay).
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
2. Calculate the distance Vijay covered within the timeframe of the faster participant's (Ajay) completion.
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
3. Compute the disparity between the total race distance and the distance covered by Vijay.
\[ \text{Defeat Margin} = \text{Total Distance} - \text{Distance covered by loser} \]
Step 3: Detailed Calculation:
Given data:
Race distance = 600 m.
Ajay's completion time = 38 seconds.
Vijay's completion time = 48 seconds.
First, calculate Vijay's speed:
\[ \text{Speed}_{\text{Vijay}} = \frac{\text{Total Distance}}{\text{Time}_{\text{Vijay}}} = \frac{600 \text{ m}}{48 \text{ s}} \]
\[ \text{Speed}_{\text{Vijay}} = 12.5 \text{ m/s} \]
Next, determine Vijay's position at the moment Ajay finishes (t = 38 seconds).
Calculate the distance Vijay covers in 38 seconds:
\[ \text{Distance}_{\text{Vijay in 38s}} = \text{Speed}_{\text{Vijay}} \times \text{Time}_{\text{Ajay}} \]
\[ \text{Distance}_{\text{Vijay in 38s}} = 12.5 \text{ m/s} \times 38 \text{ s} \]
\[ \text{Distance}_{\text{Vijay in 38s}} = 475 \text{ m} \]
This indicates that when Ajay reaches the 600 m mark, Vijay is at the 475 m mark.
The margin of Ajay's victory is calculated as:
\[ \text{Defeat Margin} = 600 \text{ m} - 475 \text{ m} = 125 \text{ m} \]
Step 4: Conclusion:
Ajay defeats Vijay by 125 meters.