A man can row upstream 36 m in 6 hours. If the speed of a man in still water is 8 km/hr, find how much he can go downstream in 10 hours -----

Options

A. 150 km
B. 80 km
C. 90 km
D. 100 km

Answer

To solve the problem step by step, we need to find out how far the man can row downstream in 10 hours.

### Step 1: Determine the speed of the man upstream.
The man can row 36 km upstream in 6 hours. To find his speed upstream, we use the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting the values:

\[ \text{Speed upstream} = \frac{36 \text{ km}}{6 \text{ hours}} = 6 \text{ km/hr} \]

### Step 2: Calculate the speed of the current (stream).
We know the speed of the man in still water is 8 km/hr. The speed of the man upstream is the speed in still water minus the speed of the current. Let \( c \) be the speed of the current.

Using the equation:

\[ \text{Speed upstream} = \text{Speed in still water} - \text{Speed of current} \]

Substituting the known values:

\[ 6 \text{ km/hr} = 8 \text{ km/hr} - c \]

Rearranging gives:

\[ c = 8 \text{ km/hr} - 6 \text{ km/hr} = 2 \text{ km/hr} \]

### Step 3: Calculate the speed of the man downstream.
The speed of the man downstream is the speed in still water plus the speed of the current:

\[ \text{Speed downstream} = \text{Speed in still water} + \text{Speed of current} \]

Substituting the values:

\[ \text{Speed downstream} = 8 \text{ km/hr} + 2 \text{ km/hr} = 10 \text{ km/hr} \]

### Step 4: Calculate the distance he can row downstream in 10 hours.
Using the speed downstream, we can find the distance he can row in 10 hours:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:

\[ \text{Distance} = 10 \text{ km/hr} \times 10 \text{ hours} = 100 \text{ km} \]

### Final Answer:
The man can row **100 km downstream in 10 hours**.

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