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 a square with given speeds on each side, we can follow these steps:

### Step 1: Understand the Problem
The aeroplane flies around a square, with each side measuring 100 miles. The speeds for each side are:
- Side 1 (A): 100 mph
- Side 2 (B): 200 mph
- Side 3 (C): 300 mph
- Side 4 (D): 400 mph

### Step 2: Calculate the Time Taken for Each Side
To find the average speed, we first need to calculate the time taken to cover each side of the square.

- Time for Side A:
\[ \text{Time}_A = \frac{\text{Distance}}{\text{Speed}} = \frac{100 \text{ miles}}{100 \text{ mph}} = 1 \text{ hour} \]

- Time for Side B:
\[ \text{Time}_B = \frac{100 \text{ miles}}{200 \text{ mph}} = 0.5 \text{ hours} \]

- Time for Side C:
\[ \text{Time}_C = \frac{100 \text{ miles}}{300 \text{ mph}} \approx 0.333 \text{ hours} \]

- Time for Side D:
\[ \text{Time}_D = \frac{100 \text{ miles}}{400 \text{ mph}} = 0.25 \text{ hours} \]

### Step 3: Calculate Total Time
Now, we sum the times taken for each side:
\[ \text{Total Time} = \text{Time}_A + \text{Time}_B + \text{Time}_C + \text{Time}_D \]
\[ \text{Total Time} = 1 + 0.5 + 0.333 + 0.25 = 2.083 \text{ hours} \]

### Step 4: Calculate Total Distance
The total distance covered by the aeroplane is the perimeter of the square:
\[ \text{Total Distance} = 4 \times 100 \text{ miles} = 400 \text{ miles} \]

### Step 5: Calculate Average Speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we calculated:
\[ \text{Average Speed} = \frac{400 \text{ miles}}{2.083 \text{ hours}} \approx 192 \text{ mph} \]

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

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