Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 50 miles per hour slower than the southbound plane. After 5 hours the planes are 2834 miles apart. Find the speed of the eastbound plane.
A)375 miles per hour
B)425 miles per hour
C)550 miles per hour
D)475 miles per hour
E)500 miles per hour

Question

Quizplus · Accepted Answer

The distance between the two planes can be represented by the Pythagorean theorem, $d = \sqrt{x^2 + (x + 50)^2}$, where $x$ is the speed of the eastbound plane and $x + 50$ is the speed of the southbound plane. After 5 hours, the eastbound plane has traveled $5x$ miles, and the southbound plane has traveled $5(x + 50)$ miles. Substituting these into the equation gives $\sqrt{(5x)^2 + [5(x + 50)]^2} = 2834$. Solving for $x$ gives the speed of the eastbound plane as 375 miles per hour.

Two Planes Leave Simultaneously from the Same Airport, One Flying