Step 1: Concept Clarification:
"Ajay defeats Vijay by X meters" indicates that when Ajay completes the race, Vijay is X meters behind the finish line. This distance is determined by calculating Vijay's progress during the time Ajay took to finish.
Step 2: Methodology:
1. Determine the speed of the slower participant (Vijay).
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
2. Calculate the distance Vijay covered within the time taken by the faster participant (Ajay).
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
3. Calculate the difference 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:
Race distance = 600 m.
Ajay's time = 38 seconds.
Vijay's 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 when Ajay finishes (at t = 38 seconds).
Calculate the distance Vijay covers in 38 seconds:
\[ \text{Distance}_{\text{Vijay in 38s}} = \text{Speed}_{\text{Vijay}} \times \text{Time}_{\text{Ajay}} \]
\[ \text{Distance}_{\text{Vijay in 38s}} = 12.5 \text{ m/s} \times 38 \text{ s} \]
\[ \text{Distance}_{\text{Vijay in 38s}} = 475 \text{ m} \]
When Ajay reaches 600 m, Vijay is at 475 m.
The defeat margin is the difference:
\[ \text{Defeat Margin} = 600 \text{ m} - 475 \text{ m} = 125 \text{ m} \]
Step 4: Conclusion:
Ajay wins against Vijay by 125 meters.