Solve.
-Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had
The eastbound car traveled?
A)15 mi
B)30 mi
C)20 mi
D)25 mi

Question

Quizplus · Accepted Answer

Let's call the distance traveled by the eastbound car "x". According to the problem, we know that:

(distance between the two cars)^2 = (distance traveled by northbound car)^2 + (distance traveled by eastbound car)^2

We also know that when the northbound car had gone 15 mi, the distance between the two cars was 5 mi more than the distance traveled by the eastbound car. So:

(distance between the two cars) = x + 5

Putting these two pieces of information together, we can write:

(x + 5)^2 = 15^2 + x^2

Simplifying this equation, we get:

x^2 + 10x - 200 = 0

Factoring, we get:

(x - 10)(x + 20) = 0

Since we're looking for a positive distance, we can ignore the negative solution and conclude that:

x = 10

So the eastbound car traveled 10 miles when the northbound car had gone 15 miles. Therefore, the eastbound car must have traveled a total of:

15 + 10 = 25 miles

The only answer choice that is close to 25 miles is C) 20 mi, but it's not exactly right. So the best choice is C) 20 mi, even though it's not the exact answer.

Solve. -Two Cars Leave an Intersection. One Car Travels North; the the Other