A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is

Options

A. 2h
B. 2h 40min
C. 1h 20min
D. cannot be estimated with the information given

Explanation

To solve the problem, we need to find the time taken for a boat to travel upstream and downstream a distance of 8 km each way, given that the velocity of the water is 4 km/h and the boat's speed in still water is derived from the information provided.

### Step-by-Step Solution:

1. **Determine the boat's speed in still water:**
- The boat takes 2 hours to travel a total distance of 16 km (8 km upstream and 8 km downstream).
- Speed of the boat in still water (V_boat) can be calculated as:
\[ V_{\text{boat}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{16 \text{ km}}{2 \text{ hours}} = 8 \text{ km/h} \]

2. **Calculate the effective speed of the boat upstream:**
- When the boat is going upstream, the effective speed is reduced by the speed of the water:
\[ V_{\text{upstream}} = V_{\text{boat}} - V_{\text{water}} = 8 \text{ km/h} - 4 \text{ km/h} = 4 \text{ km/h} \]

3. **Calculate the time taken to go upstream:**
- The time taken to travel 8 km upstream can be calculated using the formula:
\[ \text{Time}_{\text{upstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{4 \text{ km/h}} = 2 \text{ hours} \]

4. **Calculate the effective speed of the boat downstream:**
- When the boat is going downstream, the effective speed is increased by the speed of the water:
\[ V_{\text{downstream}} = V_{\text{boat}} + V_{\text{water}} = 8 \text{ km/h} + 4 \text{ km/h} = 12 \text{ km/h} \]

5. **Calculate the time taken to go downstream:**
- The time taken to travel 8 km downstream can be calculated as:
\[ \text{Time}_{\text{downstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{12 \text{ km/h}} = \frac{2}{3} \text{ hours} \approx 0.67 \text{ hours} \text{ or } 40 \text{ minutes} \]

6. **Calculate the total time for the round trip:**
- The total time taken for the journey (upstream and downstream) is:
\[ \text{Total Time} = \text{Time}_{\text{upstream}} + \text{Time}_{\text{downstream}} = 2 \text{ hours} + \frac{2}{3} \text{ hours} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \text{ hours} \approx 2 \text{ hours and } 40 \text{ minutes} \]

### Final Answer:
The total time taken for going upstream 8 km and coming back downstream is **2 hours and 40 minutes**.