A train travels at `60 km//h` for `0.50 h` , at `30 km//h` for the next `0.24 h` and at `70 km//h` for the next `0.71 h`. What is the average speed of the train ?

Options

A. 60 km/hr
B. 70 km/hr
C. 80 km/hr
D. 90 km/hr

Explanation

To find the average speed of the train, we need to calculate the total distance covered and the total time taken during its journey. The average speed can then be determined using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

### Step 1: Calculate the distance for each segment of the journey.

1. **First Segment:**
- Speed = 60 km/h
- Time = 0.50 h
- Distance = Speed × Time = \(60 \, \text{km/h} \times 0.50 \, \text{h} = 30 \, \text{km}\)

2. **Second Segment:**
- Speed = 30 km/h
- Time = 0.24 h
- Distance = Speed × Time = \(30 \, \text{km/h} \times 0.24 \, \text{h} = 7.2 \, \text{km}\)

3. **Third Segment:**
- Speed = 70 km/h
- Time = 0.71 h
- Distance = Speed × Time = \(70 \, \text{km/h} \times 0.71 \, \text{h} = 49.7 \, \text{km}\)

### Step 2: Calculate the total distance covered.

\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3 \]
\[ \text{Total Distance} = 30 \, \text{km} + 7.2 \, \text{km} + 49.7 \, \text{km} = 86.9 \, \text{km} \]

### Step 3: Calculate the total time taken.

\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 \]
\[ \text{Total Time} = 0.50 \, \text{h} + 0.24 \, \text{h} + 0.71 \, \text{h} = 1.45 \, \text{h} \]

### Step 4: Calculate the average speed.

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{86.9 \, \text{km}}{1.45 \, \text{h}} \approx 59.93 \, \text{km/h} \]

### Final Answer:
The average speed of the train is approximately **59.93 km/h**.

---