A man can row 12 km/hr in still water. If the speed of the current is 3 km/hr, he takes 4 hours more in upstream than in the downstream. What is the distance (in km)?

Options

A. 30
B. 45
C. 60
D. 90

Answer

To solve the problem, we need to find the distance the man rows, given his rowing speed in still water and the speed of the current. Here’s a step-by-step solution:

### Step 1: Define the given values
- Speed of the man in still water (M) = 12 km/hr
- Speed of the current (C) = 3 km/hr

### Step 2: Calculate the effective speeds
- Speed downstream (D) = M + C = 12 km/hr + 3 km/hr = 15 km/hr
- Speed upstream (U) = M - C = 12 km/hr - 3 km/hr = 9 km/hr

### Step 3: Let the distance be 'd' km
- Time taken to row downstream (T_down) = Distance / Speed downstream = d / 15
- Time taken to row upstream (T_up) = Distance / Speed upstream = d / 9

### Step 4: Set up the equation based on the time difference
According to the problem, the time taken to row upstream is 4 hours more than the time taken to row downstream:
\[ T_{up} = T_{down} + 4 \]
Substituting the expressions for time:
\[ \frac{d}{9} = \frac{d}{15} + 4 \]

### Step 5: Solve the equation
To eliminate the fractions, we can multiply through by the least common multiple of 9 and 15, which is 45:
\[ 45 \cdot \frac{d}{9} = 45 \cdot \frac{d}{15} + 45 \cdot 4 \]
This simplifies to:
\[ 5d = 3d + 180 \]

### Step 6: Rearranging the equation
Subtract \(3d\) from both sides:
\[ 5d - 3d = 180 \]
\[ 2d = 180 \]

### Step 7: Solve for d
Divide both sides by 2:
\[ d = \frac{180}{2} = 90 \text{ km} \]

### Conclusion
The distance the man rows is **90 km**.

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