13

Part of 2007 Stanford Mathematics Tournament

Problems(2)

SMT 2007 Team #13

Source:

Mary Jane and Rachel are playing ping pong. Rachel has a

7/8

chance of returning any shot, and Mary Jane has a

5/8

chance. Mary Jane serves to Rachel (and doesn't mess up the serve). What is the average number of returns made?

Ant Crawling up a Rope

Source:

A rope of length 10 m is tied tautly from the top of a flagpole to the ground 6 m away from the base of the pole. An ant crawls up the rope and its shadow moves at a rate of 30 cm/min. How many meters above the ground is the ant after 5 minutes? (This takes place on the summer solstice on the Tropic of Cancer so that the sun is directly overhead.)

ratiogeometrysimilar trianglesPythagorean Theorem