A' goes 10 km distance with average speed of 6 km/h while rest 20 km he travels with an average speed of 15 km/h. What is the average speed of 'A' during the whole journey?

Options

A. 10 km/h
B. 12 km/h
C. 13 km/h
D. 14.5 km/h

Answer

To find the average speed of 'A' during the whole journey, we will follow these steps:

### Step 1: Calculate the total distance
The total distance covered by A is the sum of the two segments of the journey:
- First segment: 10 km
- Second segment: 20 km

**Total Distance = 10 km + 20 km = 30 km**

### Step 2: Calculate the time taken for each segment
Next, we will calculate the time taken for each segment using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**For the first segment (10 km at 6 km/h):**
\[ \text{Time}_1 = \frac{10 \text{ km}}{6 \text{ km/h}} = \frac{10}{6} \text{ hours} = \frac{5}{3} \text{ hours} \]

**For the second segment (20 km at 15 km/h):**
\[ \text{Time}_2 = \frac{20 \text{ km}}{15 \text{ km/h}} = \frac{20}{15} \text{ hours} = \frac{4}{3} \text{ hours} \]

### Step 3: Calculate the total time
Now, we will find the total time taken for the journey by adding the time for both segments:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 \]
\[ \text{Total Time} = \frac{5}{3} \text{ hours} + \frac{4}{3} \text{ hours} = \frac{5 + 4}{3} \text{ hours} = \frac{9}{3} \text{ hours} = 3 \text{ hours} \]

### Step 4: Calculate the average speed
Finally, we can calculate the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Speed} = \frac{30 \text{ km}}{3 \text{ hours}} = 10 \text{ km/h} \]

### Final Answer:
The average speed of 'A' during the whole journey is **10 km/h**.

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