A man rows 750 m in 775 seconds against the stream and return in `7(1)/(2)` minutes . What is rowing speed in still water ?

Options

A. 4.7 km/hr
B. 4 km/hr
C. 3.5 km/hr
D. 6 km/hr

Explanation

To solve the problem step by step, let's break it down as follows:

### Step 1: Calculate the upstream speed
The man rows 750 meters against the stream in 775 seconds.

To find the speed (upstream speed), we use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

So,
\[ \text{Upstream Speed} = \frac{750 \text{ m}}{775 \text{ s}} \]

Calculating this gives:
\[ \text{Upstream Speed} = \frac{750}{775} \approx 0.9677 \text{ m/s} \]

### Step 2: Convert the return time to seconds
The man returns in \( 7 \frac{1}{2} \) minutes.

First, convert this to seconds:
\[ 7 \frac{1}{2} \text{ minutes} = 7.5 \text{ minutes} = 7.5 \times 60 \text{ seconds} = 450 \text{ seconds} \]

### Step 3: Calculate the downstream speed
Now, he rows the same distance (750 meters) downstream in 450 seconds.

Using the same speed formula:
\[ \text{Downstream Speed} = \frac{750 \text{ m}}{450 \text{ s}} \]

Calculating this gives:
\[ \text{Downstream Speed} = \frac{750}{450} \approx 1.6667 \text{ m/s} \]

### Step 4: Calculate the speed in still water
The speed in still water can be calculated using the formula:
\[ \text{Speed in Still Water} = \frac{\text{Upstream Speed} + \text{Downstream Speed}}{2} \]

Substituting the values we found:
\[ \text{Speed in Still Water} = \frac{0.9677 + 1.6667}{2} \]

Calculating this gives:
\[ \text{Speed in Still Water} = \frac{2.6344}{2} \approx 1.3172 \text{ m/s} \]

### Step 5: Convert the speed to kilometers per hour
To convert from meters per second to kilometers per hour, we multiply by \( 18/5 \):
\[ \text{Speed in km/h} = 1.3172 \times \frac{18}{5} \]

Calculating this gives:
\[ \text{Speed in km/h} \approx 4.7 \text{ km/h} \]

### Final Answer
The rowing speed in still water is approximately **4.7 km/h**.

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