Question 203559
The two lines of travel can be represented by the two legs of a right triangle.
Let's find the distance each plane will travel between 1:00pm and 3:00 pm.
This is 2 hours of travel, so the plane traveling north at 150 mph will have gone 300 miles in 2 hours (150mph X 2hrs = 300 mi.) while the plane traveling westward will have gone 400 miles in 2 hours (200mph X 2hrs = 400 mi.)
Their distance apart after 2 hours can be represented by the hypotenuse (c) of the right triangle and this distance can be found using the Pythagorean theorem: {{{c^2 = a^2+b^2}}}.
{{{c^2 = (300)^2+(400)^2}}}
{{{c^2 = 90000+160000}}}
{{{c^2 = 250000}}} Take the square root of both sides.
{{{highlight(c = 500)}}}
The two planes will be 500 miles apart at 3:00pm