Question

An aeroplane leaves an airport and flies due north at a speed of 300 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 400 km/hr. How far apart will be the two planes after `1 1/2` hours?

Answer 1

Given: Two planes depart same airport simultaneously: one due north at 300 km/hr, the other due west at 400 km/hr, time = `1 1/2` hours (1.5 hr).

Step-wise calculation:

1. Time = `1 1/2` hr

= 1.5 hr

2. Distance north = 300 km/hr × 1.5 hr

= 450 km

3. Distance west = 400 km/hr × 1.5 hr

= 600 km

4. The two distances form perpendicular legs. 

So use Pythagoras: separation² = 450² + 600² 

= 202500 + 360000 

= 562500

5. Separation = `sqrt(562500)`

= 750 km

After `1 1/2` hours the two planes are 750 km apart.