If two planes leave the same airport at 100 PM how many mile

If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?

Solution

Distance covered by the plane moving north in 2 hrs = 150 * 2
= 300 miles
Distance covered by the plane moving west in 2 hrs = 200 * 2
= 400 miles
So at 3 PM both the planes would have covered the above distances.
We know that North and West are perpendicular to each other.
So by Pythagorean theorem,
distance between them = sqrt(300^2 + 400^2)
= sqrt(900 + 1600)
= sqrt(2500)
= 50
THus they are 50 miles at 3 PM