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Algebra Difficulty 4.3 AIME Find the answer United States

Problem:

Two cars are driving directly towards each other such that one is twice as fast as the other. The distance between their starting points is $4$ miles. When the two cars meet, how many miles is the faster car from its starting point?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Note that the faster car traveled twice the distance of the slower car, and together, the two cars traveled the total distance between the starting points, which is $4$ miles. Let the distance that the faster car traveled be $x$ . Then,

$x + \frac{x}{2} = 4 \Longrightarrow x = \frac{8}{3}.$

Thus, the faster car traveled $\frac{8}{3}$ miles from the starting point.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.