## Elementary Algebra

Aaron catches up with Andy after $\frac{2}{3}$ hours.
Let t represent the time it takes Aaron to catch up with Andy. Since Aaron starts walking one­-half hour later than Andy; this means that Andy walks one-half hour more than Aaron. Since Aaron walks t hours, Andy walks t + 0.5 hours. Andy walks at 2 miles per hour, for a distance of (t + 0.5) $\times$ 2 = 2t + 1 miles. Aaron walks at 3.5 miles per hour, for a distance of t$\times$ 3.5 = 3.5t miles. Since Aaron catch up with Andy, the distances they travel must be equal. So we can set up the following equation: 2t + 1 = 3.5t 1.5t = 1 Divide both sides by 1.5 t = $\frac{2}{3}$ Aaron catches up with Andy after $\frac{2}{3}$ hours.