A boat running upstream covers a distance of 10 km in 30 min and while running downstream, it covers the same distance in 25 min. What is the speed of the river current (in km/h)?

Options

A. a. 20
B. b. `2.2`
C. c. `2`
D. d. Couldn't be determined

Answer

To find the speed of the river current, we can follow these steps:

### Step 1: Calculate the speed of the boat upstream.
- The boat covers a distance of 10 km in 30 minutes.
- To convert 30 minutes into hours, we use the conversion:
\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]
- Now, we can calculate the speed:
\[ \text{Speed upstream} = \frac{\text{Distance}}{\text{Time}} = \frac{10 \text{ km}}{0.5 \text{ hours}} = 20 \text{ km/h} \]

### Step 2: Calculate the speed of the boat downstream.
- The boat covers the same distance of 10 km in 25 minutes.
- Convert 25 minutes into hours:
\[ 25 \text{ minutes} = \frac{25}{60} \text{ hours} \approx 0.4167 \text{ hours} \]
- Now, calculate the speed:
\[ \text{Speed downstream} = \frac{\text{Distance}}{\text{Time}} = \frac{10 \text{ km}}{0.4167 \text{ hours}} \approx 24 \text{ km/h} \]

### Step 3: Set up the equations for the speeds.
- Let the speed of the boat in still water be \( b \) km/h and the speed of the river current be \( r \) km/h.
- From the upstream speed:
\[ b - r = 20 \quad \text{(1)} \]
- From the downstream speed:
\[ b + r = 24 \quad \text{(2)} \]

### Step 4: Solve the equations.
- Add equations (1) and (2):
\[ (b - r) + (b + r) = 20 + 24 \]
\[ 2b = 44 \implies b = 22 \text{ km/h} \]
- Now substitute \( b \) back into equation (1):
\[ 22 - r = 20 \implies r = 2 \text{ km/h} \]

### Conclusion:
The speed of the river current is \( \mathbf{2 \text{ km/h}} \).

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