speed 2 jets flying at right angles to each other

[RPMACS]

Need help placing in a formula please.

A military jet flies directly over and at right angles to the straight-line course of a commercial jet. The military jet is flying 200 mph faster than four times the commercial jet. How fast is each going if they are 2050 miles apart (on a direct line) after 1 hour?

 

[galactus]

Let \(\displaystyle R_{c}\) be the rate of the commercial jet and \(\displaystyle R_{m}\) the rate of the military jet.

Since d=rt, then the commercial has traveled \(\displaystyle R_{c}(1)\) miles

and the military has traveled \(\displaystyle (4R_{c}+200)(1)\).....[1]

This is a right triangle with hypoteneuse 2050

\(\displaystyle (R_{c})^{2}+(4R_{c}+200)^{2}=2050^{2}\)

Solve for \(\displaystyle R_{c}\), then you can find \(\displaystyle R_{m}\) by plugging back into [1]