Question 990307
Two boats leave the buoy at the same time.
 One of the boats travels north at a rate of N miles per hour, and the other boat travels east at a rate of 4N miles per hour.
 What is the distance between the boats 30 minutes after both boats leave the buoy? 
:
Find the distances they travel in .5 hrs (30 min). Dist = speed * time
North: .5n
East: .5(4n) = 2n
:
This is a pythag problem; a^2 + b^2 = c^2; where
a = .5n
b = 2n
c = the distance between them
c^2 = (.5n)^2 + (2n)^2
c^2 = .25n^2 + 4n^2
like terms
c^2 = 4.25n^2
c = {{{sqrt(4.25n^2)}}}
Factor inside the radical to reveal perfect squares
c = {{{.25*17*n^2)}}}
Extract the square root of those
c = {{{.5n*sqrt(17)}}} or about 2.06 miles apart after 30 min