1. ## Linear Equation Help

An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back, averaging 240km/h for the outward trip and 320km/h for the return trip. If the plane was away for 35 minutes, find the distance, x km.

2. We know that velocity = distance / time.

So time = distance / velocity.

So $\frac{x}{240} + \frac{x}{320} = 35mins = \frac{35}{60}
hrs$

$\Rightarrow \frac{4x}{960} + \frac{3x}{960} = \frac{35}{60}$

$\Rightarrow 7x = \frac{35}{60} \times 960$

$\Rightarrow 7x = 560$

$\Rightarrow x = 80\, km$