A boatman can row 2 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current.

Options

A. `1/3` km//hr
B. `2/3` km//hr
C. `5/3` km//hr
D. `3 km//hr`

Answer

To solve the problem step by step, we need to find the rate of the current based on the boatman's rowing times against and with the stream.

### Step-by-Step Solution:

1. **Convert Time to Hours**:
- The boatman rows 2 km against the stream in 20 minutes.
- Convert 20 minutes to hours:
\[ 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \]

2. **Calculate Upstream Speed**:
- Speed is calculated as distance divided by time.
- The upstream speed (against the current) is:
\[ \text{Upstream Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ km}}{\frac{1}{3} \text{ hours}} = 2 \times 3 = 6 \text{ km/h} \]

3. **Convert Return Time to Hours**:
- The boatman returns downstream in 18 minutes.
- Convert 18 minutes to hours:
\[ 18 \text{ minutes} = \frac{18}{60} \text{ hours} = \frac{3}{10} \text{ hours} \]

4. **Calculate Downstream Speed**:
- The downstream speed (with the current) is:
\[ \text{Downstream Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ km}}{\frac{3}{10} \text{ hours}} = 2 \times \frac{10}{3} = \frac{20}{3} \text{ km/h} \]

5. **Calculate the Speed of the Current**:
- Let the speed of the current be \( S \).
- The relationship between upstream speed, downstream speed, and current speed is:
\[ \text{Downstream Speed} = \text{Upstream Speed} + S \]
- Rearranging gives:
\[ S = \text{Downstream Speed} - \text{Upstream Speed} \]
- Substitute the values:
\[ S = \frac{20}{3} \text{ km/h} - 6 \text{ km/h} \]
- Convert 6 km/h to a fraction with a common denominator:
\[ 6 = \frac{18}{3} \text{ km/h} \]
- Now calculate \( S \):
\[ S = \frac{20}{3} - \frac{18}{3} = \frac{2}{3} \text{ km/h} \]

6. **Final Answer**:
- The rate of the current is \( \frac{2}{3} \text{ km/h} \).