A man can row at 14 km/hr. in still water and speed of stream is 2 km/hr. If it takes him 3.5 hr. to row to a place & to come back, then find how far is the place?

Options

A. 36 km
B. 48 km
C. 28 km
D. 24 km

Answer

To solve the problem step by step, we will use the information given about the man's rowing speed in still water and the speed of the stream.

### Step 1: Identify the speeds
- Speed of the man in still water (x) = 14 km/hr
- Speed of the stream (y) = 2 km/hr

### Step 2: Calculate the effective speeds
- When rowing upstream (against the stream), the effective speed = x - y = 14 km/hr - 2 km/hr = 12 km/hr
- When rowing downstream (with the stream), the effective speed = x + y = 14 km/hr + 2 km/hr = 16 km/hr

### Step 3: Let the distance to the place be 'd' km
- Time taken to row upstream = Distance / Speed = d / 12 hours
- Time taken to row downstream = Distance / Speed = d / 16 hours

### Step 4: Total time for the round trip
- Total time = Time upstream + Time downstream = (d / 12) + (d / 16)

### Step 5: Set up the equation
- We know that the total time taken for the round trip is 3.5 hours. Therefore, we can set up the equation:
\[ \frac{d}{12} + \frac{d}{16} = 3.5 \]

### Step 6: Find a common denominator
- The least common multiple of 12 and 16 is 48. We will convert the fractions:
\[ \frac{d}{12} = \frac{4d}{48} \quad \text{and} \quad \frac{d}{16} = \frac{3d}{48} \]
So, the equation becomes:
\[ \frac{4d + 3d}{48} = 3.5 \]
\[ \frac{7d}{48} = 3.5 \]

### Step 7: Solve for 'd'
- Multiply both sides by 48:
\[ 7d = 3.5 \times 48 \]
Calculating the right side:
\[ 3.5 \times 48 = 168 \]
So we have:
\[ 7d = 168 \]
Now, divide both sides by 7:
\[ d = \frac{168}{7} = 24 \text{ km} \]

### Final Answer
The distance to the place is **24 km**.

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