A man swims downstream a distance of 15 km in 1 hour . If the speed of the current is 5km/hour by the man to swim the same distance up - stream is

Options

A. 1 hours 30 minutes
B. 45 minutes
C. 2 hours 30 minutes
D. 3 hours

Answer

To solve the problem step by step, we need to determine the time it takes for a man to swim upstream after swimming downstream.

### Step 1: Understand the given information
- Distance swum downstream = 15 km
- Time taken to swim downstream = 1 hour
- Speed of the current = 5 km/h

### Step 2: Calculate the speed of the man in still water
The speed of the man while swimming downstream can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

So, the speed of the man downstream is:
\[ \text{Speed}_{\text{downstream}} = \frac{15 \text{ km}}{1 \text{ hour}} = 15 \text{ km/h} \]

### Step 3: Determine the speed of the man in still water
The speed of the man in still water can be calculated using the formula:
\[ \text{Speed}_{\text{still water}} = \text{Speed}_{\text{downstream}} - \text{Speed}_{\text{current}} \]

Substituting the known values:
\[ \text{Speed}_{\text{still water}} = 15 \text{ km/h} - 5 \text{ km/h} = 10 \text{ km/h} \]

### Step 4: Calculate the speed of the man while swimming upstream
When swimming upstream, the effective speed of the man is:
\[ \text{Speed}_{\text{upstream}} = \text{Speed}_{\text{still water}} - \text{Speed}_{\text{current}} \]

So:
\[ \text{Speed}_{\text{upstream}} = 10 \text{ km/h} - 5 \text{ km/h} = 5 \text{ km/h} \]

### Step 5: Calculate the time taken to swim upstream
To find the time taken to swim upstream, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the known values:
\[ \text{Time}_{\text{upstream}} = \frac{15 \text{ km}}{5 \text{ km/h}} = 3 \text{ hours} \]

### Conclusion
The man will take **3 hours** to swim the same distance upstream.

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