1. A woman throws a sƟck into a lake for her dog to fetch; the sƟck is 15 feet down the shore line and 30 feet into the water from there. The dog may jump directly into the water and swim, or run along the shore line to get closer to the sƟck before swimming. The dog runs about 22ft/s and swims about 1.5ft/s. How far along the shore should the dog run to minimize theƟme it takes to get to the stick?
shore_distance_swum <- sqrt(900 /483)

shore_distance_run <- 15- shore_distance_swum

water_distance <- 30

hypot <- sqrt(water_distance^2 + shore_distance_swum^2)

runtime <- shore_distance_run / 22
swimtime <-  hypot / 1.5

The dog should run along the shore for 13.6349527 feet and them jump in the lake and swim 30.0310398 feet. This should get our pup to the stick in 20.6404638 seconds, comprised of 0.6197706 seconds running and 20.0206932 seconds swimming - Mark Spitz he’s not.


  1. Google “calculus dog” to learn more about a dog’s ability to minimize times.

  1. Bonus Video - Enjoy