SOLUTION: A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles.

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Question 828522: A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously form the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?
Answer by KMST(5328) About Me  (Show Source):
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If R= radius of each circle, the rectangle's length and width should be 4R and 2R respectively.

The perimeter of the rectangle is 2%2A%284R%2B2R%29=2%2A6R=12R
That is the distance A runs in one lap.
The circumference of a circle is 2pi%2AR ,
and the distance that B runs in one lap is
2%2A%282pi%2AR%29=4pi%2AR , which is longer than 12R .
How much longer?
The difference is 4pi%2AR-12R and as a fraction of 12R it is
=4.7%
So B must run 4.7% more distance in the same time.
B must be 4.7% faster than A.