Solve the problem.
-Two cars travel at right angles to each other from an intersection until they are 10 miles apart. At that point, one car has gone 2 mi farther than the other. How far did the slower car travel?
A) 12 mi
B) 6 mi
C) 8 mi
D) 4 mi

Question

Quizplus · Accepted Answer

The slower car traveled 6 miles. Let x be the distance traveled by the slower car, then the faster car traveled x + 2 miles. Since they are traveling at right angles, we can use the Pythagorean theorem: $x^2 + (x + 2)^2 = 10^2$. Solving this equation gives $x^2 + x^2 + 4x + 4 = 100$, or $2x^2 + 4x - 96 = 0$. Dividing the entire equation by 2 gives $x^2 + 2x - 48 = 0$, which factors to $(x + 8)(x - 6) = 0$. Thus, $x = 6$ or $x = -8$, but distance cannot be negative, so $x = 6$ miles.

Solve the Problem. -Two Cars Travel at Right Angles to Each Other from Each