A plane flying north at 500 mph passes over a city at 12 noon. A plane flying east at the same altitude passes over the same city at 12.30 pm. The plane is flying east at 400 mph. To the nearest hundred miles, how far apart are the two planes at 2 pm ?

Solution(By Examveda Team)

Distance covered by the first plane till 2 pm, i.e., in 2 hrs :
= (500 × 2) miles
= 1000 miles
Distance covered by the second plane till 2 pm, i.e., in $$1\frac{1}{2}$$ hrs :
= $$\left( {400 \times \frac{3}{2}} \right)$$   miles
= 600 miles
∴ Required distance :
$$\eqalign{ & = AB \cr & = \sqrt {{{\left( {1000} \right)}^2} + {{\left( {600} \right)}^2}} \cr & = \sqrt {1000000 + 360000} \cr & = \sqrt {1360000} {\text{ miles}} \cr & {\text{ = 200}}\sqrt {34} {\text{ miles}} \cr & {\text{ = 1160 miles}} \approx {\text{1200 miles}} \cr} $$