This file will help you to investigate which is the quickest path for the Taco Cart Problem posed by Dan Meyer at his blog dy/dan. It also lets you investigate the problem if the two people are going at different speeds on the sand and the path. Click on the picture below to try it out.

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Nice work! I like how you made the two points travel along the two paths. I may have to add that to the one I made. Here is mine. https://www.desmos.com/calculator/zkgbh6sowy