A man travels from point A to B at 40 km/hr and returns from B to A at 60 km/hr. What is his average speed during the whole journey?

Options

A. 55 km/hr
B. 45 km/hr
C. 48 km/hr
D. 50 km/hr

Answer

To find the average speed of the man during the whole journey from point A to B and back from B to A, we can follow these steps:

### Step 1: Define the Distance
Let the distance from point A to point B be \( L \) kilometers.

### Step 2: Calculate Total Distance
The total distance for the round trip (A to B and back to A) is:
\[ \text{Total Distance} = L + L = 2L \]

### Step 3: Calculate Time Taken for Each Leg of the Journey
- Time taken to travel from A to B at 40 km/hr:
\[ \text{Time}_{A \to B} = \frac{L}{40} \]

- Time taken to travel from B to A at 60 km/hr:
\[ \text{Time}_{B \to A} = \frac{L}{60} \]

### Step 4: Calculate Total Time
The total time for the journey is the sum of the time taken for each leg:
\[ \text{Total Time} = \text{Time}_{A \to B} + \text{Time}_{B \to A} = \frac{L}{40} + \frac{L}{60} \]

To add these fractions, we need a common denominator. The least common multiple of 40 and 60 is 120.
\[ \text{Total Time} = \frac{3L}{120} + \frac{2L}{120} = \frac{5L}{120} = \frac{L}{24} \]

### Step 5: Calculate Average Speed
Average speed is defined as total distance divided by total time:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2L}{\frac{L}{24}} \]

### Step 6: Simplify the Average Speed Calculation
\[ \text{Average Speed} = 2L \times \frac{24}{L} = 48 \text{ km/hr} \]

Thus, the average speed during the whole journey is **48 km/hr**.

### Summary of Steps:
1. Define the distance from A to B as \( L \).
2. Calculate the total distance for the round trip as \( 2L \).
3. Calculate the time taken for each leg of the journey.
4. Find the total time for the journey.
5. Use the formula for average speed to find the average speed.