A river 2 km wide is flowing at the rate of 2km/hr. A boatman, can row the boat at a speed of 4 km/hr in still water, goes a distance of 2 km upstream and them comes back. The time taken by him to complete his journey is

Options

A. 60 minutes
B. 70 minutes
C. 80 minutes
D. 90 minutes

Explanation

To solve the problem of the boatman's journey across the river, we will break it down step by step.

### Step 1: Understand the problem
The boatman rows a boat across a river that is 2 km wide, with a river current flowing at 2 km/hr. The boatman's rowing speed in still water is 4 km/hr. He rows 2 km upstream and then returns back downstream.

### Step 2: Calculate the effective speed upstream
When the boatman rows upstream, he is rowing against the current. Therefore, we need to subtract the speed of the river from the speed of the boat.

- Speed of the boat in still water = 4 km/hr
- Speed of the river current = 2 km/hr

Effective speed upstream = Speed of the boat - Speed of the river
\[ \text{Effective speed upstream} = 4 \text{ km/hr} - 2 \text{ km/hr} = 2 \text{ km/hr} \]

### Step 3: Calculate the effective speed downstream
When the boatman rows downstream, he is rowing with the current. Thus, we need to add the speed of the river to the speed of the boat.

Effective speed downstream = Speed of the boat + Speed of the river
\[ \text{Effective speed downstream} = 4 \text{ km/hr} + 2 \text{ km/hr} = 6 \text{ km/hr} \]

### Step 4: Calculate the time taken to row upstream
The distance the boatman rows upstream is 2 km. We can use the formula for time, which is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Time taken to row upstream:
\[ \text{Time upstream} = \frac{2 \text{ km}}{2 \text{ km/hr}} = 1 \text{ hour} \]

### Step 5: Calculate the time taken to row downstream
Now, we calculate the time taken to row downstream using the same formula.

Time taken to row downstream:
\[ \text{Time downstream} = \frac{2 \text{ km}}{6 \text{ km/hr}} = \frac{1}{3} \text{ hour} \]

### Step 6: Calculate the total time taken for the journey
Now we add the time taken for both upstream and downstream journeys to find the total time taken.

Total time:
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} \]
\[ \text{Total time} = 1 \text{ hour} + \frac{1}{3} \text{ hour} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ hours} \]

### Step 7: Convert total time into minutes
To convert the time from hours to minutes, we multiply by 60 (since 1 hour = 60 minutes).

\[ \text{Total time in minutes} = \frac{4}{3} \text{ hours} \times 60 \text{ minutes/hour} = 80 \text{ minutes} \]

### Final Answer
The total time taken by the boatman to complete his journey is **80 minutes**.

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