An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after hours?

Let A be the first aeroplane flied due north at a speed of 1000 km/hr and B be the second aeroplane flied due west at a speed of 1200 km/hr

Distance covered by plane A in 1.5 hrs = 1000 × 32 = 1500km

Distance covered by plane B in 1.5 hrs = 1200 × 32 = 1800km

Now, in right triangle ABC

By using Pythagoras theorem, we have

AB² = BC² + AC²

⇒ AB² = (1800)² + (1500)²

⇒ AB² = 3240000 + 2250000

⇒ AB² = 5490000

⇒ AB = 300√61 km