A boat goes a certain distance at 30 km/hr and comes back the same distance at 60 km/hr .what is the average speed (in km /hr for the total journey ?

Options

A. 45
B. 50
C. 40
D. 35

Answer

To find the average speed of a boat that travels a certain distance at two different speeds, we can use the formula for average speed when the distance is constant. Here’s a step-by-step solution:

### Step 1: Identify the speeds
The boat travels at two different speeds:
- Speed while going: \( S_1 = 30 \) km/hr
- Speed while returning: \( S_2 = 60 \) km/hr

### Step 2: Use the average speed formula
When the distance is the same for both journeys, the average speed \( V_{avg} \) can be calculated using the formula:
\[ V_{avg} = \frac{2 \cdot S_1 \cdot S_2}{S_1 + S_2} \]

### Step 3: Substitute the values into the formula
Substituting the values of \( S_1 \) and \( S_2 \):
\[ V_{avg} = \frac{2 \cdot 30 \cdot 60}{30 + 60} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:
\[ 2 \cdot 30 \cdot 60 = 3600 \]
Calculating the denominator:
\[ 30 + 60 = 90 \]

### Step 5: Divide the numerator by the denominator
Now, we divide the numerator by the denominator:
\[ V_{avg} = \frac{3600}{90} \]

### Step 6: Simplify the fraction
Simplifying \( \frac{3600}{90} \):
\[ V_{avg} = 40 \text{ km/hr} \]

### Conclusion
The average speed for the total journey is \( 40 \) km/hr.

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