An aeroplane covers a certain distance at a speed of 320 km/h in ` 5 (1)/(2)` hours . To cover the same distance in 4 hours . it must travel at a speed of

Options

A. 460 km / h
B. 440 km/h
C. 420 km/h
D. 450 km/h

Answer

To solve the problem, we need to find the speed required for the aeroplane to cover the same distance in 4 hours that it previously covered in 5.5 hours at a speed of 320 km/h.

### Step-by-Step Solution:

1. **Calculate the Distance Covered**:
- The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Given speed = 320 km/h and time = 5.5 hours, we can calculate the distance:
\[ \text{Distance} = 320 \, \text{km/h} \times 5.5 \, \text{hours} \]
- Performing the multiplication:
\[ \text{Distance} = 320 \times 5.5 = 1760 \, \text{km} \]

2. **Determine the Required Speed**:
- Now, we need to find the speed required to cover the same distance (1760 km) in 4 hours.
- Using the distance formula again, we rearrange it to find speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Substituting the known values:
\[ \text{Speed} = \frac{1760 \, \text{km}}{4 \, \text{hours}} \]
- Performing the division:
\[ \text{Speed} = 440 \, \text{km/h} \]

### Final Answer:
The aeroplane must travel at a speed of **440 km/h** to cover the same distance in 4 hours.