A man rows downstream 60 km and upstream 36 km, taking 4 hours each time. The speed of the man is :

Options

A. 15 km/h
B. 16 km/h
C. 8 km/h
D. 12 km/h

Answer

To solve the problem, we need to determine the speed of the man rowing downstream and upstream. We will use the information given in the question to set up equations based on the speeds.

### Step-by-step Solution:

1. **Define Variables:**
Let the speed of the man in still water be \( x \) km/h and the speed of the stream be \( y \) km/h.

2. **Set Up Equations:**
- When rowing downstream, the effective speed is \( x + y \).
- When rowing upstream, the effective speed is \( x - y \).

3. **Downstream Equation:**
The man rows 60 km downstream in 4 hours. We can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Thus, for downstream:
\[ x + y = \frac{60 \text{ km}}{4 \text{ hours}} = 15 \text{ km/h} \]
This gives us our first equation:
\[ (1) \quad x + y = 15 \]

4. **Upstream Equation:**
The man rows 36 km upstream in 4 hours. Using the same formula:
\[ x - y = \frac{36 \text{ km}}{4 \text{ hours}} = 9 \text{ km/h} \]
This gives us our second equation:
\[ (2) \quad x - y = 9 \]

5. **Solve the System of Equations:**
We can add equations (1) and (2):
\[ (x + y) + (x - y) = 15 + 9 \]
Simplifying this, we get:
\[ 2x = 24 \]
Dividing both sides by 2:
\[ x = 12 \text{ km/h} \]

6. **Conclusion:**
The speed of the man in still water is \( 12 \) km/h.