An aeroplane flys around squares whose all sides are of length `100` miles. If the aeroplane covers at a speed of `100 mph` the first side, `200 mph` the second side `300 mph` the third side and `400 mph` the fourth side. The average speed of aeroplane around the square is

Options

A. `190mph`
B. `195mph`
C. `192mph`
D. `200mph`

Explanation

To find the average speed of the aeroplane flying around the square, we will use the concept of the harmonic mean since the distances covered are the same for each side but at different speeds.

### Step-by-Step Solution:

1. **Identify the Length of Each Side:**
Each side of the square is given as 100 miles.

2. **Identify the Speeds for Each Side:**
- Speed on the first side = 100 mph
- Speed on the second side = 200 mph
- Speed on the third side = 300 mph
- Speed on the fourth side = 400 mph

3. **Calculate the Time Taken for Each Side:**
- Time for the first side = Distance / Speed = \( \frac{100}{100} = 1 \) hour
- Time for the second side = Distance / Speed = \( \frac{100}{200} = 0.5 \) hours
- Time for the third side = Distance / Speed = \( \frac{100}{300} \approx 0.3333 \) hours
- Time for the fourth side = Distance / Speed = \( \frac{100}{400} = 0.25 \) hours

4. **Calculate the Total Time Taken:**
Total time = Time for first side + Time for second side + Time for third side + Time for fourth side
\[ \text{Total Time} = 1 + 0.5 + 0.3333 + 0.25 = 2.0833 \text{ hours} \]

5. **Calculate the Total Distance:**
Since there are 4 sides and each side is 100 miles, the total distance is:
\[ \text{Total Distance} = 4 \times 100 = 400 \text{ miles} \]

6. **Calculate the Average Speed:**
Average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{400}{2.0833} \approx 192 \text{ mph} \]

### Final Answer:
The average speed of the aeroplane around the square is approximately **192 mph**.

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