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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

While Mary Poppins waits to be taken from Terminal A to Terminal J by a moving platform, Jane and Michael avoid boredom by running to the end of the platform and then back to Mary and so on until the group finally reaches the end of the platform. The platform is 0.2 miles long and moves at a speed of 1.5 miles per hour. Jane runs at a speed of 4 miles per hour and Michael runs at a speed of 4.5 miles per hour. What is the positive difference between the number of miles covered by Jane and the number of miles covered by Michael?

(characters from P.L. Travers - "Mary Poppins")

Since we know the time it takes for the moving platform to take group from Terminal A to Terminal J:

equation

we know the total time Jane and Michael had in which to do their running:

Jane covered:

equation

Michael covered:

equation

and the positive difference is:

equation