math challenge

Week of January 13 - 19, 1997

Bugs On the Go

Grassy and Woody, a grasshopper and a woodbug, made a New Year's resolution to be more ambitious. Tired of creeping around their miserable abode, these bugs wanted to move up in the world.

The desired destination is the summit of a small mound, exactly 20 cm away from where Grassy and Woody are sitting.

Grassy moves 1 millimeter in one minute, and then pauses for a minute before starting again. He keeps up this method of locomotion for his entire journey.

Woody keeps up a steady pace of 2/3 millimeter per minute.

If both start at the same time, and each has to go the same distance, who will arrive at their destination first, and by how many seconds?

See the solutions