# An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after $$3\over 2$$ hours.

## Solution :

Let the first plane starts from O and goes upto A towards north.

Where OA = ($$1000 \times {3\over 2}$$) km = 1500 km

Let the second plane starts from O at the same time and goes upto B towards west, where OB = ($$1200 \times {3\over 2}$$) km = 1800 km

According to the question, the required distance = BA.

In right triangle ABC, by Pythagoras theorem, we have :

$${AB}^2$$ = $${OA}^2$$ + $${OB}^2$$

= $$(1500)^2$$ + $$(1800)^2$$

= 2250000 + 3240000

= 5490000

AB = $$3\times 100\sqrt{61}$$ = $$300\sqrt{61}$$.