A man can row 8 km/hr in still water. If the speed of the current is 4 km/hr, he takes 8 hours more in upstream than in the downstream. What is the distance (in km)?

Options

A. 24
B. 48
C. 36
D. 72

Answer

To solve the problem step by step, we will use the information given about the speeds of rowing in still water and the current, as well as the time difference between upstream and downstream travel.

### Step 1: Identify the speeds
- Speed of the boat in still water = 8 km/hr
- Speed of the current = 4 km/hr

### Step 2: Calculate the effective speeds
- **Upstream speed** = Speed of boat - Speed of current = 8 km/hr - 4 km/hr = 4 km/hr
- **Downstream speed** = Speed of boat + Speed of current = 8 km/hr + 4 km/hr = 12 km/hr

### Step 3: Set up the time equations
Let the distance be \( d \) km. The time taken to travel upstream and downstream can be expressed as:
- Time taken upstream = \( \frac{d}{\text{Upstream speed}} = \frac{d}{4} \) hours
- Time taken downstream = \( \frac{d}{\text{Downstream speed}} = \frac{d}{12} \) hours

### Step 4: Set up the equation based on the time difference
According to the problem, the time taken upstream is 8 hours more than the time taken downstream:
\[ \frac{d}{4} = \frac{d}{12} + 8 \]

### Step 5: Solve the equation
To eliminate the fractions, we can multiply the entire equation by 12 (the least common multiple of 4 and 12):
\[ 12 \cdot \frac{d}{4} = 12 \cdot \frac{d}{12} + 12 \cdot 8 \]
This simplifies to:
\[ 3d = d + 96 \]
Now, subtract \( d \) from both sides:
\[ 3d - d = 96 \]
\[ 2d = 96 \]
Now, divide by 2:
\[ d = 48 \]

### Conclusion
The distance is **48 km**.

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