Solve the following word problem.

The average speed of a Falcon drone is $\frac{7}{5}$ times the average speed of a Hawk drone. A cargo carrier covers 240 km in 5 hours. If the speed of the Hawk drone is $\frac{3}{2}$ times the speed of the cargo carrier, then how much distance will the Falcon drone cover in 2 hours.

The correct answer is 201.6 km.

We are given three flying objects — a Falcon drone, a Hawk drone, and a cargo carrier — with relationships between their speeds. Let's work through this step by step.

Step 1: Find the speed of the cargo carrier.

The cargo carrier covers 240 km in 5 hours. Using the basic formula:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}=\frac{240}{5}=48\text{km/h}$

So, the speed of the cargo carrier is 48 km/h.

Step 2: Find the speed of the Hawk drone.

The Hawk drone's speed is $\frac{3}{2}$ times the speed of the cargo carrier:

$\text{Speed of Hawk}=\frac{3}{2}\times 48=\frac{144}{2}=72\text{km/h}$

So, the speed of the Hawk drone is 72 km/h.

Step 3: Find the speed of the Falcon drone.

The Falcon drone's speed is $\frac{7}{5}$ times the speed of the Hawk drone:

$\text{Speed of Falcon}=\frac{7}{5}\times 72=\frac{504}{5}=100.8\text{km/h}$

So, the speed of the Falcon drone is 100.8 km/h.

Step 4: Calculate the distance the Falcon drone covers in 2 hours.

Using the distance formula:

$\text{Distance}=\text{Speed}\times \text{Time}=100.8\times 2=201.6\text{km}$

Therefore, the Falcon drone will cover 201.6 km in 2 hours.