Question

An aeroplane flies with an average speed of 756 km/h. A helicopter takes 48 h to cover twice the distance covered by aeroplane in 9 h. How much distance will the helicopter cover in 18 h ?
(Assuming that flights are non-stop and moving with uniform speed.)

• A. 5010 km
• B. 4875 km
• C. 5760 km
• D. 5103 km

Answer 1

The Correct Option is D

To solve the problem, we need to determine the distance covered by the helicopter in 18 hours. Begin by calculating the distance the aeroplane covers in 9 hours:

Step 1: Calculate the distance covered by the aeroplane in 9 hours.

The speed of the aeroplane is 756 km/h. Therefore, the distance covered in time \( t \) (hours) is given by the formula:

\( \text{Distance} = \text{Speed} \times \text{Time} \)

For 9 hours:

\( \text{Distance}_{\text{plane}} = 756 \, \text{km/h} \times 9 \, \text{h} = 6804 \, \text{km} \)

Step 2: Calculate the total distance covered by the helicopter in 48 hours.

The helicopter travels twice the distance covered by the aeroplane in the same 9 hours, which is:

\( 2 \times 6804 \, \text{km} = 13608 \, \text{km} \)

So, in 48 hours, the helicopter covers 13608 km.

Step 3: Determine the speed of the helicopter.

Using the formula for speed:

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{13608 \, \text{km}}{48 \, \text{h}} = 283.5 \, \text{km/h} \)

Step 4: Calculate the distance the helicopter covers in 18 hours.

Using the helicopter's speed, the distance covered in 18 hours is:

\( \text{Distance}_{\text{helicopter in 18 h}} = 283.5 \, \text{km/h} \times 18 \, \text{h} = 5103 \, \text{km} \)

Thus, the helicopter will cover 5103 km in 18 hours.