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 Math Central Quandaries & Queries
 Question from Zoe: Amy and Joey are situated on a circular track 400 feet around. Joey starts running at a rate of 10 feet per second. Amy waits for a full minute, then starts running from the same point (in the same direction) at 12 feet per second. How many seconds elapse before Amy passes Joey on the track?

Hi Zoe,

Imagine that the track is on a large rotating platform, with the track rotating at the rate of 10 feet per second.The circumference of the track is 400 feet.

Joey steps on the track and stands still for 1 minute. Where is Joey on the platform after 1 minute?

At this instant Amy steps on the track and starts to run at 2 feet per second.You are standing off to the side so to you it looks like Joey is moving at 10 feet per second and Amy is moving at the rate of 12 feet per second. From Amy's point of view Joey is standing still and she is moving at the rate of 2 feet per second. How long will it take Amy to catch up to Joey?

Penny