If the speed of a boat in still water is 7.5 km/h and the speed of the stream is 2.5 km/h , then find the total time required for the boat to travel 30 km upstream and 30 km downstream .

Answer

To solve the problem of finding the total time required for the boat to travel 30 km upstream and 30 km downstream, we can follow these steps:

### Step 1: Determine the speeds
- **Speed of the boat in still water** = 7.5 km/h
- **Speed of the stream** = 2.5 km/h

### Step 2: Calculate the effective speed upstream
When the boat is traveling upstream, it moves against the current of the stream. Therefore, the effective speed upstream can be calculated as:
\[ \text{Effective speed upstream} = \text{Speed of the boat} - \text{Speed of the stream} \]
\[ \text{Effective speed upstream} = 7.5 \text{ km/h} - 2.5 \text{ km/h} = 5 \text{ km/h} \]

### Step 3: Calculate the time taken to travel upstream
The time taken to travel a certain distance can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
For the upstream journey:
\[ \text{Time upstream} = \frac{30 \text{ km}}{5 \text{ km/h}} = 6 \text{ hours} \]

### Step 4: Calculate the effective speed downstream
When the boat is traveling downstream, it moves with the current of the stream. Therefore, the effective speed downstream can be calculated as:
\[ \text{Effective speed downstream} = \text{Speed of the boat} + \text{Speed of the stream} \]
\[ \text{Effective speed downstream} = 7.5 \text{ km/h} + 2.5 \text{ km/h} = 10 \text{ km/h} \]

### Step 5: Calculate the time taken to travel downstream
Using the same formula for time:
\[ \text{Time downstream} = \frac{30 \text{ km}}{10 \text{ km/h}} = 3 \text{ hours} \]

### Step 6: Calculate the total time
Now, we can find the total time required for the boat to travel both upstream and downstream:
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} \]
\[ \text{Total time} = 6 \text{ hours} + 3 \text{ hours} = 9 \text{ hours} \]

### Final Answer:
The total time required for the boat to travel 30 km upstream and 30 km downstream is **9 hours**.

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