A car covers a certain distance travelling at a speed of 60 kmph and returns to the starting point at a speed of 40 kmph. Find the average speed for the entire journey

Answer

To find the average speed for the entire journey of the car, we can follow these steps:

### Step 1: Define the distance
Let the distance covered by the car in one direction be \( s \) kilometers.

### Step 2: Calculate the time taken for each part of the journey
- When traveling to the destination at a speed of 60 km/h, the time taken \( t_1 \) is given by:
\[ t_1 = \frac{s}{60} \]

- When returning to the starting point at a speed of 40 km/h, the time taken \( t_2 \) is given by:
\[ t_2 = \frac{s}{40} \]

### Step 3: Calculate the total distance
The total distance for the entire journey (to the destination and back) is:
\[ \text{Total Distance} = s + s = 2s \]

### Step 4: Calculate the total time
The total time for the entire journey is:
\[ \text{Total Time} = t_1 + t_2 = \frac{s}{60} + \frac{s}{40} \]

### Step 5: Find a common denominator for the total time
The least common multiple of 60 and 40 is 120. We can express \( t_1 \) and \( t_2 \) with a common denominator:
\[ t_1 = \frac{s}{60} = \frac{2s}{120} \]
\[ t_2 = \frac{s}{40} = \frac{3s}{120} \]
Thus,
\[ \text{Total Time} = \frac{2s}{120} + \frac{3s}{120} = \frac{5s}{120} = \frac{s}{24} \]

### Step 6: Calculate the average speed
The average speed \( V_{avg} \) is given by:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2s}{\frac{s}{24}} = 2s \times \frac{24}{s} = 48 \text{ km/h} \]

### Final Answer
The average speed for the entire journey is **48 km/h**.

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