Motion System Design

# Fun with fundamentals: 253

Problem #253: Tag, you’re it
Better move faster than the proverbial tortoise on this one.

The herpetologist Norman Eggenbrecker brims over with ambition, but is missing a few marbles. When assigned to summer research on the Galapagos Islands, Norman botched tortoise taggings, marking males as females and vice versa. After a few more conservation debacles, he was demoted to Booga Booga, a small, lesser known volcanic island, to tag the giant checkerback turtle. Though often overshadowed by the biodiversity of the nearby Galapagos, Booga Booga has several unusual species found no place else on Earth. One such species is the Anatidae vocalicus, a black and white bird that flies at a constant 10 mph. Known by islanders as the “chatty jailbird,” the gooselike fowl puts any parrot to shame with its conversation skills.

In a rare stroke of genius, Norman made a deal with one. He asked the bird to find an untagged turtle. Norman’s camp was set up 12.5 miles from the seashore. The bird flew straight from it toward the seashore, and in two hours returned with message that it had found a turtle moving toward the sea at a constant 0.5 mph. Norman immediately scampered after the turtle at a steady 4 mph knowing that if the turtle reached the sea, he would not be able to catch it.

The bird flew nonstop between the hunter and the turtle. Each odd flight, it turned back after reaching the target and reported the remaining distance. Each even flight, the bird turned upon reaching the seashore to report how far the turtle was from the sea.

Norman promised to reward the bird with a gumdrop for every ten miles of flight and five bonus gumdrops if the turtle mission was successful – not very nutritious, but effective. How many gumdrops did Norman owe the bird upon capturing the turtle?

Solution to problem 252, November, 2001: Snail tale