a jogging park has two identical circular tracks touching each other and rectangular track enclosing the two circles.The edges of the rectangles are tangential to circles.A and B start simultaneously from the point where one of the circular track 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 the starting point?

1) 3.88%
2) 4.22%
3) 4.44%
4) 4.72%

• 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.
• 8 years agoHelpfull: Yes(0) No(0)