It will take Nancy 1.25 hours to overtake Kirk.
Work Step by Step
Let t represent the time it will take Nancy to catch Kirk. Since Kirk starts jogging half an hour earlier, he jogs for t+0.5. Kirk jogs at 5 miles per hour, so he jogs for a distance equal to (t + 0.5) $\times$ 5 = 5t + 2.5 Nancy jogs at 7 miles per hour, which means that she travels for a distance equal to t $\times$ 7 = 7t. Because Nancy is to overtake Kirk, the distances must be equal. So: 5t + 2.5 = 7t 2t = 2.5 Divide both sides by 2. t = 1.25 It will take Nancy 1.25 hours to overtake Kirk.