SOLUTION: Amy and Betty start riding bicycles from the opposite ends of a diameter of a circular track with length 200 meters counter clockwise. Amy's speed is 6 meters/sec, and Betty's spee

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Question 1163495: Amy and Betty start riding bicycles from the opposite ends of a diameter of a circular track with length 200 meters counter clockwise. Amy's speed is 6 meters/sec, and Betty's speed is 5 m/s. Amy catches up Betty how many times in 16 minutes?
Found 2 solutions by Edwin McCravy, Boreal:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Since Amy goes 6 m/s and Betty goes 5 m/s, the curved arc distance between
them shrinks by 6-5 = 1 m/s, with Amy gaining on Betty. 

Amy gains on Betty 1 arc meter per second.

Amy starts out 100 arc meters behind Betty
So Amy will catch up to Betty the first time in 100 seconds.
Thereafter, Amy will catch up to Betty every 200 seconds.

There are 16∙60=960 seconds in 16 minutes.

Let n be the number of catch-ups Betty will make after the first one.

So 100 + n*200 <= 960
          200n <= 860
             n <= 4.3

So Betty will make 4 more catchups after the first, or 5 catch-ups.

Answer: 5

Edwin
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
16 minutes is 960 sec and Amy will go 5760 m and Betty 4800 m during that time. Amy will go 28.8 laps and Betty 24 laps.
She will catch her 5 times, because she is starting a half a lap ahead (for purposes of catching)
She is catching up at 1 m/sec and in 960 seconds she will catch up 960 m, which is 4.8 laps. From Amy's view, she will have finished her 28th lap and gone past Betty's starting and ending point, 24 laps.
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