Subodh and Hari run a race. Subodh gives Hari a start of 10 m and is beaten by almost 10 m. Who has a higher speed between the two ?

Options

A. Subodh
B. Hari
C. Both have equal speeds
D. Cannot be determined

Answer

To solve the problem, we need to analyze the information given about Subodh and Hari's race.

### Step-by-Step Solution:

1. **Understanding the Race Setup**:
- Subodh gives Hari a head start of 10 meters. This means that when the race starts, Hari is already 10 meters ahead of Subodh.

2. **Outcome of the Race**:
- It is stated that Subodh is beaten by almost 10 meters. This means that when Hari finishes the race, Subodh is still 10 meters behind him.

3. **Distance Covered**:
- Let's assume the total distance of the race is \( D \) meters.
- Since Hari has a 10-meter head start, he runs \( D \) meters while Subodh runs \( D + 10 \) meters (because he has to cover the extra distance to catch up).

4. **Conclusion About Their Speeds**:
- Since both runners finish the race at the same time, we can set up the relationship between their speeds:
- Let \( v_H \) be the speed of Hari and \( v_S \) be the speed of Subodh.
- The time taken by both to finish the race is the same.
- Therefore, we can write:
\[ \frac{D}{v_H} = \frac{D + 10}{v_S} \]

5. **Analyzing the Speed Relationship**:
- Rearranging the equation gives us:
\[ v_H = \frac{D \cdot v_S}{D + 10} \]
- Since both runners finish the race at the same time, and given that Hari had a head start and still finished ahead, we can conclude that Hari must have a higher speed than Subodh.

### Final Conclusion:
- **Who has a higher speed?**
- Hari has a higher speed than Subodh.