A jogger runs on a path at a speed of 0.075 miles per minute. A second jogger starts 5 minutes later from the same spot, but runs at a rate of 0.1 miles per minute. Create a pair of parametric equations to represent the paths of the joggers. How far down the path from the starting point does the second runner overtake the first runner?

Let t be the number of minutes since the first jogger starts. Their positions are x₁ = 0.075t and x₂ = 0.1(t − 5), where the second equation applies after the second jogger starts at t = 5. Set the positions equal to find when they meet: 0.075t = 0.1(t − 5), so t = 20 minutes. The meeting point is 0.075(20) = 1.5 miles from the start, so the answer is 1.5 miles.

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