Two men start together to walk to a certain destination one at 3.75 km an hour and another at 3 km an hour the former arrives half an hour before the later the distance is

Options

A. A)9.5km
B. B)8km
C. C)7.5km
D. D)6 km

Answer

To solve the problem, we need to find the distance to the destination based on the speeds of the two men and the time difference in their arrivals.

### Step-by-Step Solution:

1. **Define Variables:**
Let the distance to the destination be \( D \) kilometers. The speeds of the two men are:
- Man A: \( 3.75 \) km/h
- Man B: \( 3 \) km/h

2. **Calculate Time Taken:**
The time taken by each man to reach the destination can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Time taken by Man A:
\[ T_A = \frac{D}{3.75} \]
- Time taken by Man B:
\[ T_B = \frac{D}{3} \]

3. **Set Up the Equation:**
According to the problem, Man A arrives half an hour (0.5 hours) before Man B. Therefore, we can set up the equation:
\[ T_B - T_A = 0.5 \]
Substituting the expressions for \( T_A \) and \( T_B \):
\[ \frac{D}{3} - \frac{D}{3.75} = 0.5 \]

4. **Find a Common Denominator:**
The common denominator for \( 3 \) and \( 3.75 \) is \( 15 \):
- Convert \( \frac{D}{3} \) to have a denominator of 15:
\[ \frac{D}{3} = \frac{5D}{15} \]
- Convert \( \frac{D}{3.75} \) to have a denominator of 15:
\[ \frac{D}{3.75} = \frac{4D}{15} \]

5. **Substitute Back into the Equation:**
Now, substituting back into the equation gives:
\[ \frac{5D}{15} - \frac{4D}{15} = 0.5 \]
Simplifying this:
\[ \frac{D}{15} = 0.5 \]

6. **Solve for \( D \):**
To find \( D \), multiply both sides by 15:
\[ D = 0.5 \times 15 = 7.5 \]

### Final Answer:
The distance \( D \) to the destination is **7.5 km**.

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