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 for the total journey, we can use the formula for average speed when the distances are the same but the speeds are different. The average speed can be calculated using the formula:

\[ \text{Average Speed} = \frac{2 \cdot v_1 \cdot v_2}{v_1 + v_2} \]

where \( v_1 \) is the speed for the first part of the journey and \( v_2 \) is the speed for the return journey.

### Step 1: Identify the speeds
In this case:
- \( v_1 = 30 \) km/hr (speed going)
- \( v_2 = 60 \) km/hr (speed returning)

### Step 2: Substitute the values into the formula
Substituting the values into the average speed formula:

\[ \text{Average Speed} = \frac{2 \cdot 30 \cdot 60}{30 + 60} \]

### Step 3: Calculate the numerator
Calculate the numerator:

\[ 2 \cdot 30 \cdot 60 = 3600 \]

### Step 4: Calculate the denominator
Calculate the denominator:

\[ 30 + 60 = 90 \]

### Step 5: Calculate the average speed
Now, substitute the values back into the formula:

\[ \text{Average Speed} = \frac{3600}{90} \]

Calculating this gives:

\[ \text{Average Speed} = 40 \text{ km/hr} \]

### Final Answer
The average speed for the total journey is **40 km/hr**.

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