Jatin goes to a place at a speed of 5 km/hr and return home at speed of 10 km/hr. What is his average speed (in km/hr)?

Options

A. 6.5
B. 6.8
C. 6.67
D. 8

Answer

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

### Step 1: Define the distance
Let's assume the distance to the place is \( d \) kilometers.

### Step 2: Calculate the time taken to go to the place
The speed while going to the place is 5 km/hr. Therefore, the time taken to go to the place can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{d}{5} \text{ hours} \]

### Step 3: Calculate the time taken to return home
The speed while returning home is 10 km/hr. Therefore, the time taken to return home can be calculated as:
\[ \text{Time} = \frac{d}{10} \text{ hours} \]

### Step 4: Calculate the total time for the round trip
The total time for the entire journey (going and returning) is the sum of the time taken to go and the time taken to return:
\[ \text{Total Time} = \frac{d}{5} + \frac{d}{10} \]
To add these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 10 is 10. Thus, we can rewrite the first term:
\[ \frac{d}{5} = \frac{2d}{10} \]
Now we can add:
\[ \text{Total Time} = \frac{2d}{10} + \frac{d}{10} = \frac{3d}{10} \text{ hours} \]

### Step 5: Calculate the total distance
The total distance for the round trip is:
\[ \text{Total Distance} = d + d = 2d \text{ kilometers} \]

### Step 6: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2d}{\frac{3d}{10}} \]
To simplify this, we multiply by the reciprocal of the total time:
\[ \text{Average Speed} = 2d \times \frac{10}{3d} = \frac{20}{3} \text{ km/hr} \]

### Step 7: Convert to decimal
Calculating \( \frac{20}{3} \):
\[ \frac{20}{3} \approx 6.67 \text{ km/hr} \]

### Final Answer
Thus, Jatin's average speed for the entire journey is approximately **6.67 km/hr**.

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