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 determine the time taken by a boat to travel upstream and downstream given the velocity of the boat in still water and the velocity of the water current.

### Step 1: Calculate the speed of the boat in still water
We know that the boat takes 2 hours to travel a total distance of 16 km (8 km upstream and 8 km downstream).

- **Distance traveled** = 8 km (upstream) + 8 km (downstream) = 16 km
- **Total time taken** = 2 hours

Using the formula for speed:
\[ \text{Speed of the boat (VB)} = \frac{\text{Total distance}}{\text{Total time}} = \frac{16 \text{ km}}{2 \text{ hours}} = 8 \text{ km/h} \]

### Step 2: Identify the velocity of water
The velocity of water is given as:
\[ \text{Velocity of water (VW)} = 4 \text{ km/h} \]

### Step 3: Calculate the time taken to go upstream
When the boat is going upstream, the effective speed of the boat is reduced by the speed of the water. Therefore, the speed of the boat upstream (V_upstream) is:
\[ V_{\text{upstream}} = V_B - V_W = 8 \text{ km/h} - 4 \text{ km/h} = 4 \text{ km/h} \]

Now, we calculate the time taken to travel 8 km upstream (T1):
\[ T_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{4 \text{ km/h}} = 2 \text{ hours} \]

### Step 4: Calculate the time taken to come downstream
When the boat is coming downstream, the effective speed of the boat is increased by the speed of the water. Therefore, the speed of the boat downstream (V_downstream) is:
\[ V_{\text{downstream}} = V_B + V_W = 8 \text{ km/h} + 4 \text{ km/h} = 12 \text{ km/h} \]

Now, we calculate the time taken to travel 8 km downstream (T2):
\[ T_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{12 \text{ km/h}} = \frac{2}{3} \text{ hours} \approx 0.67 \text{ hours} \]

### Step 5: Calculate the total time taken
The total time taken for the entire journey (upstream and downstream) is:
\[ T = T_1 + T_2 = 2 \text{ hours} + \frac{2}{3} \text{ hours} = 2 \text{ hours} + 0.67 \text{ hours} = 2.67 \text{ hours} \]

To convert this into hours and minutes:
\[ 2.67 \text{ hours} = 2 \text{ hours} + 0.67 \times 60 \text{ minutes} = 2 \text{ hours} + 40 \text{ minutes} \]

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

---