A train has a speed of `60 km//h` for the first one hour and `40 k/h` for the next half hour. Its average speed in `km//h` is

Options

A. 50
B. `53.33`
C. 48
D. 70

Answer

To find the average speed of the train, we can follow these steps:

### Step 1: Calculate the total time taken
The train travels for two segments:
- First segment: 1 hour
- Second segment: 0.5 hours (which is half an hour)

Total time taken (T) = 1 hour + 0.5 hours = 1.5 hours = \( \frac{3}{2} \) hours

### Step 2: Calculate the distance covered in each segment
1. **First segment (d1)**:
- Speed = 60 km/h
- Time = 1 hour
- Distance covered (d1) = Speed × Time = \( 60 \, \text{km/h} \times 1 \, \text{h} = 60 \, \text{km} \)

2. **Second segment (d2)**:
- Speed = 40 km/h
- Time = 0.5 hours
- Distance covered (d2) = Speed × Time = \( 40 \, \text{km/h} \times 0.5 \, \text{h} = 20 \, \text{km} \)

### Step 3: Calculate the total distance covered
Total distance (D) = d1 + d2 = \( 60 \, \text{km} + 20 \, \text{km} = 80 \, \text{km} \)

### Step 4: Calculate the average speed
Average speed (V_avg) is defined as the total distance divided by the total time taken.

\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{80 \, \text{km}}{\frac{3}{2} \, \text{h}} = 80 \, \text{km} \times \frac{2}{3} = \frac{160}{3} \, \text{km/h} \]

### Final Answer
The average speed of the train is \( \frac{160}{3} \, \text{km/h} \) or approximately \( 53.33 \, \text{km/h} \).

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