An aeroplane covers the distance of 2500 km, 1600 km and 500 km at a speed of 500 km/h, 400 km/h and 250 km/h respectively. Find the average speed of the aeroplane.

Options

A. `418 (2)/(11)` km/hr
B. 420 km/hr
C. `421 (2)/(11)` km/hr
D. 418 km/hr

Answer

To find the average speed of the aeroplane, we will follow these steps:

### Step 1: Write down the distances and speeds
The aeroplane covers the following distances at the given speeds:
- Distance 1: 2500 km at a speed of 500 km/h
- Distance 2: 1600 km at a speed of 400 km/h
- Distance 3: 500 km at a speed of 250 km/h

### Step 2: Calculate the time taken for each distance
We can calculate the time taken for each segment using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

- **Time for Distance 1**:
\[ \text{Time}_1 = \frac{2500 \text{ km}}{500 \text{ km/h}} = 5 \text{ hours} \]

- **Time for Distance 2**:
\[ \text{Time}_2 = \frac{1600 \text{ km}}{400 \text{ km/h}} = 4 \text{ hours} \]

- **Time for Distance 3**:
\[ \text{Time}_3 = \frac{500 \text{ km}}{250 \text{ km/h}} = 2 \text{ hours} \]

### Step 3: Calculate the total distance and total time
Now, we will add up all the distances and all the times:

- **Total Distance**:
\[ \text{Total Distance} = 2500 \text{ km} + 1600 \text{ km} + 500 \text{ km} = 4600 \text{ km} \]

- **Total Time**:
\[ \text{Total Time} = 5 \text{ hours} + 4 \text{ hours} + 2 \text{ hours} = 11 \text{ hours} \]

### Step 4: Calculate the average speed
Now we can find the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values we calculated:
\[ \text{Average Speed} = \frac{4600 \text{ km}}{11 \text{ hours}} \approx 418.18 \text{ km/h} \]

### Final Answer
The average speed of the aeroplane is approximately **418.18 km/h**.

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