3470.21 – Distance in flight

You and a friend each pilot a jet plane starting from the same spot in Michigan at exactly noon on a Thursday. You travel due east at $x$ kilometers per hour, and your friend travels due south at $y$ kilometers per hour. Use the Pythagorean Theorem to devise a formula for $d$, the distance in kilometers between your two planes after $t$ hours of flight. Assume the two planes remain at the same height.

Solution

This is one of those problems where it helps a great deal to discard the useless information and simply draw a picture. Below is the one I made. Isn't it lovely? It suggests the following formulas:

$$d^2 = (xt)^2 + (yt)^2,$$

$$d = t \cdot \sqrt{x^2 + y^2}.$$