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# An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after $${1} {\dfrac{1}{2}}$$ hours?

Given,
Speed of first aeroplane = 1000 km/hr

Distance covered by first aeroplane flying due north in

$${1} {\dfrac{1}{2}}$$ hours = 100 × $$\frac{3}{2}$$ km = 1500 km

Speed of second aeroplane = 1200 km/hr

Distance covered by second aeroplane flying due west in

$${1} {\dfrac{1}{2}}$$ hours (OB) = 1200 × $$\frac{3}{2}$$ km = 1800 km

In right angle $$\triangle$$ AOB, by Pythagoras Theorem,
$$\Rightarrow AB^2 = AO^2 + OB^2$$
$$\Rightarrow AB^2 = (1500)^2 + (1800)^2$$
$$\Rightarrow AB = \sqrt {(2250000 + 3240000)}$$
$$\Rightarrow AB = \sqrt{5490000}$$
$$\Rightarrow$$ AB = $$300 \sqrt{61}$$ km