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 P.M. The plane is flying east to 400 mph. To the nearest hundred miles, how far apart are the two planes at 2 P.M.?

Distance covered by the first plane till 2 P.M.
i.e., in 2 hrs = (500 × 2) miles
= 1000 miles.
Distance covered by the second plane till 2 P.M.
i.e., in 1(1/2) hrs = (400 × 3/2) miles
= 600 miles.
∴ Required distance
= AB =√{(1000)² + (600)²}
=√(1000000 + 360000)
=√1360000
= 200√34 miles
= 200 × 5.83
= 1166 miles.