An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is `250 km h^(-1)` , along BC `500 km h^(-1)` , along CD `200 km h^(-1)` , and along DA 100 km `h^(-1)` , Its average speed (in km `h^(-1)` ) over the entire trip is

Options

A. 225.5
B. 175.5
C. 125.5
D. 190.5

Explanation

To find the average speed of the aeroplane flying around the square field ABCD, we will follow these steps:

### Step 1: Calculate the total distance traveled
The aeroplane flies around a square field with each side measuring 1000 km. Therefore, the total distance traveled around the square is the perimeter of the square.

\[ \text{Total Distance} = 4 \times \text{side length} = 4 \times 1000 \text{ km} = 4000 \text{ km} \]

### Step 2: Calculate the time taken for each segment of the trip
We will calculate the time taken for each leg of the journey using the formula:

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

- **From A to B:**
- Distance = 1000 km
- Speed = 250 km/h
\[ T_{AB} = \frac{1000 \text{ km}}{250 \text{ km/h}} = 4 \text{ hours} \]

- **From B to C:**
- Distance = 1000 km
- Speed = 500 km/h
\[ T_{BC} = \frac{1000 \text{ km}}{500 \text{ km/h}} = 2 \text{ hours} \]

- **From C to D:**
- Distance = 1000 km
- Speed = 200 km/h
\[ T_{CD} = \frac{1000 \text{ km}}{200 \text{ km/h}} = 5 \text{ hours} \]

- **From D to A:**
- Distance = 1000 km
- Speed = 100 km/h
\[ T_{DA} = \frac{1000 \text{ km}}{100 \text{ km/h}} = 10 \text{ hours} \]

### Step 3: Calculate the total time taken
Now, we sum up the time taken for each segment:

\[ \text{Total Time} = T_{AB} + T_{BC} + T_{CD} + T_{DA} \]
\[ \text{Total Time} = 4 \text{ hours} + 2 \text{ hours} + 5 \text{ hours} + 10 \text{ hours} = 21 \text{ hours} \]

### Step 4: Calculate the average speed
Now that we have the total distance and total time, we can calculate the average speed using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Speed} = \frac{4000 \text{ km}}{21 \text{ hours}} \approx 190.48 \text{ km/h} \]

### Conclusion
Thus, the average speed of the aeroplane over the entire trip is approximately **190.48 km/h**.

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