The speed of a stream is 3 km / hr and the speed of man in still water is 5 km /hr .The time taken by the man to swim 26 km downstream is :

Options

A. `8(2)/(3)` hrs .
B. `3(1)/(4)` hrs
C. 13 hrs .
D. `5(1)/(5)` hrs

Answer

To solve the problem of how long it takes for a man to swim 26 km downstream, we can follow these steps:

### Step 1: Understand the speeds involved
- The speed of the stream (current) = 3 km/hr
- The speed of the man in still water = 5 km/hr

### Step 2: Calculate the effective speed downstream
When swimming downstream, the man's effective speed is the sum of his speed in still water and the speed of the stream:
\[ \text{Effective Speed Downstream} = \text{Speed of Man} + \text{Speed of Stream} \]
\[ \text{Effective Speed Downstream} = 5 \text{ km/hr} + 3 \text{ km/hr} = 8 \text{ km/hr} \]

### Step 3: Use the formula for time
The formula to calculate time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is 26 km and the effective speed downstream is 8 km/hr.

### Step 4: Substitute the values into the formula
\[ \text{Time} = \frac{26 \text{ km}}{8 \text{ km/hr}} \]

### Step 5: Perform the calculation
\[ \text{Time} = \frac{26}{8} = 3.25 \text{ hours} \]
This can also be expressed as:
\[ \text{Time} = 3 \text{ hours and } 15 \text{ minutes} \]

### Final Answer
The time taken by the man to swim 26 km downstream is **3.25 hours** or **3 hours and 15 minutes**.

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