A bus covers the first 10km of its journey at an average speed of 40 km/h and the remaining 45 km at an speed of 60 km/h. The average speed of the bus for its total journey is

Options

A. 52.5 km/h
B. 50 km/h
C. 57.5 km/h
D. 55 km/h

Answer

To find the average speed of the bus for its total journey, we will follow these steps:

### Step 1: Calculate the total distance traveled by the bus.
The bus covers two segments of the journey:
- First segment: 10 km
- Second segment: 45 km

**Total Distance = 10 km + 45 km = 55 km**

### Step 2: Calculate the time taken for each segment of the journey.
To find the time taken for each segment, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**For the first segment:**
- Distance = 10 km
- Speed = 40 km/h
\[ \text{Time}_1 = \frac{10 \text{ km}}{40 \text{ km/h}} = \frac{1}{4} \text{ hours} = 0.25 \text{ hours} \]

**For the second segment:**
- Distance = 45 km
- Speed = 60 km/h
\[ \text{Time}_2 = \frac{45 \text{ km}}{60 \text{ km/h}} = \frac{3}{4} \text{ hours} = 0.75 \text{ hours} \]

### Step 3: Calculate the total time taken for the journey.
**Total Time = Time for first segment + Time for second segment**
\[ \text{Total Time} = 0.25 \text{ hours} + 0.75 \text{ hours} = 1 \text{ hour} \]

### Step 4: Calculate the average speed of the bus.
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Using the values we calculated:
\[ \text{Average Speed} = \frac{55 \text{ km}}{1 \text{ hour}} = 55 \text{ km/h} \]

### Final Answer:
The average speed of the bus for its total journey is **55 km/h**.

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