On a skating plane, Michel and Jennie are in a distance of a mile on each side of a point. They are going to skate to the direction of each other’s. Jennie, having added force with the flow of the wind, skated two and one-half miles faster than Michel and beat her 6 minutes. What are the times taken by both of them?

• d = rt
  where d is distance, r is rate of speed, and t is time.
  For both skaters, distance = 1 mile.
  Given: Jennie: 1 = 2.5r(t - 6)
  Michel: 1 = rt
  For Jennie's situation, solving for rate:r = d/t2.5r = 1/(t - 6) // using substitution
  r = 1/2.5(t - 6) // divide by 2.5r = 1/(2.5t - 15) // Jennie's rate (in miles/minute)Next, substitute Jennie's rate for Michel's rate and solve for time:t = d/rt = 1/(1/(2.5t - 15)) // using substitutiont = 2.5t - 15 // from here on out, simplify equationt - 2.5t = -15 -1.5t = -15t = 10 //
  Michel's time (in minutes)Jennie's time is t -6, therefore:
  Jennie took 4 minutes and Michel took 10 minutes.
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• 18 mins and 12 mins
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