Two men start from points A and B respectively, 42 km apart. One walks from A to B at 4 km/hr and another walks from B to A at a certain uniform speed. They meet each other after 6 hours. Find the speed of the second man.

Options

A. 3 km/hr
B. 5 km/hr
C. 7 km/hr
D. 8 km/hr

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We have two men starting from points A and B, which are 42 km apart. One man walks from A to B at a speed of 4 km/hr, and the other man walks from B to A at an unknown speed. They meet after 6 hours.

### Step 2: Calculate the distance traveled by the first man
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

For the first man:
- Speed = 4 km/hr
- Time = 6 hours

So, the distance traveled by the first man is:
\[ \text{Distance} = 4 \, \text{km/hr} \times 6 \, \text{hours} = 24 \, \text{km} \]

### Step 3: Calculate the distance traveled by the second man
Since the total distance between A and B is 42 km, we can find the distance traveled by the second man by subtracting the distance traveled by the first man from the total distance:
\[ \text{Distance traveled by second man} = 42 \, \text{km} - 24 \, \text{km} = 18 \, \text{km} \]

### Step 4: Calculate the speed of the second man
Now we can find the speed of the second man using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For the second man:
- Distance = 18 km
- Time = 6 hours

So, the speed of the second man is:
\[ \text{Speed} = \frac{18 \, \text{km}}{6 \, \text{hours}} = 3 \, \text{km/hr} \]

### Final Answer
The speed of the second man is **3 km/hr**.

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