kamal goes to a place at a speed of 10 km/hr and return home at speed of 20 km/hr. What is his average speed (in km/hr)?

Answer

To find Kamal's average speed for the entire journey, we can follow these steps:

### Step 1: Define the distance
Let the distance from Kamal's home to the destination be \( x \) kilometers.

### Step 2: Calculate time taken to go to the destination
Kamal travels to the destination at a speed of 10 km/hr. The time taken to go from home to the destination (A to B) can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{10} \]
Let’s denote this time as \( t_1 \):
\[ t_1 = \frac{x}{10} \]

### Step 3: Calculate time taken to return home
On the return journey, Kamal travels back home at a speed of 20 km/hr. The time taken to return (B to A) can be calculated similarly:
\[ t_2 = \frac{x}{20} \]

### Step 4: Calculate total distance and total time
The total distance covered during the entire journey (going and returning) is:
\[ \text{Total Distance} = x + x = 2x \]
The total time taken for the entire journey is:
\[ \text{Total Time} = t_1 + t_2 = \frac{x}{10} + \frac{x}{20} \]
To add these fractions, we need a common denominator, which is 20:
\[ t_1 = \frac{x}{10} = \frac{2x}{20} \]
Thus,
\[ \text{Total Time} = \frac{2x}{20} + \frac{x}{20} = \frac{3x}{20} \]

### Step 5: Calculate average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2x}{\frac{3x}{20}} \]
Simplifying this expression:
\[ \text{Average Speed} = 2x \times \frac{20}{3x} = \frac{40}{3} \text{ km/hr} \]

### Final Answer
Thus, Kamal's average speed for the entire journey is:
\[ \text{Average Speed} = \frac{40}{3} \text{ km/hr} \approx 13.33 \text{ km/hr} \]

---