For a boat to reach port B from port A, it has to travel 80 km upstream and then 240 km downstream. If the speed of the boat in still water is 45 km/h and the speed of the stream is 5 km/h ,then what is the time taken by the boat to reach port B from port A ?

Answer

To solve the problem of how long it takes for the boat to travel from port A to port B, we will break it down into two parts: the upstream journey and the downstream journey.

### Step-by-Step Solution:

1. **Identify the speeds**:
- Speed of the boat in still water = 45 km/h
- Speed of the stream = 5 km/h

2. **Calculate the effective speed upstream**:
- When going upstream, the effective speed of the boat is reduced by the speed of the stream.
- Effective speed upstream = Speed of the boat - Speed of the stream
- Effective speed upstream = 45 km/h - 5 km/h = 40 km/h

3. **Calculate the time taken to travel upstream**:
- Distance to travel upstream = 80 km
- Time = Distance / Speed
- Time taken upstream = 80 km / 40 km/h = 2 hours

4. **Calculate the effective speed downstream**:
- When going downstream, the effective speed of the boat is increased by the speed of the stream.
- Effective speed downstream = Speed of the boat + Speed of the stream
- Effective speed downstream = 45 km/h + 5 km/h = 50 km/h

5. **Calculate the time taken to travel downstream**:
- Distance to travel downstream = 240 km
- Time taken downstream = Distance / Speed
- Time taken downstream = 240 km / 50 km/h = 4.8 hours

6. **Calculate the total time taken for the journey**:
- Total time = Time taken upstream + Time taken downstream
- Total time = 2 hours + 4.8 hours = 6.8 hours

### Final Answer:
The total time taken by the boat to reach port B from port A is **6.8 hours**.

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