How fast is each plane traveling?

Question

Two planes leave simultaneously from Chicago's O'Hare Airport, one flying north and the other east. The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours, the planes are d=2229 miles apart. Find the speed of each plane. (Round to the nearest whole number).

Answer 1

This is a trig / algebra 2 problem that will have you utilize algebra and the pythagorean theorem. I highly suggest drawing out a triangle. The two sides of the triangle are the distance traveled by each plane, while the hypotenuse is 2229 miles. The northbound plane has flown 3 * (x + 50) miles after 3 hours, where x is the speed of the eastbound plane. The eastbound plane has traveled 3*x miles.

 

So the sides of the triangle are: side 1 is 3*x + 150 miles, side 2 is 3*x miles, side 3 is 2229 miles.

 

The three sides must obey the pythagorean theorem (a^2 + b^2 = c^2), so then we plug in (3x + 150)² + (3x)² = 2229². 

 

From there it's just expanding and solving. It takes a minute, and you might want to use a calculator.

 

18x^2 + 900x + 22500 = 4968441