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2014-11-19T16:33:16+08:00

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 If\ Sean\ runs\ 20\ mph... \\ He\ will\ reach\ the\ goal\ within\ 1\ hour\ and\ 30\ minutes. \\ \\ If\ Barry\ runs\ 15\ mph... \\ He\ will\ reach\ the\ goal\ within\ 2\ hours. \\ \\ 1\ hour\ and\ 30\ minutes\ subtracted\ to\ 2\ hours=30\ minutes \\ \\ Let\ x\ be\ the\total\ miles\ of\ Barry\ when\ Sean\ reach\ the\ goal \\ Let\ y=15\ miles \\ Let\ z=30\ minutes \\ \\ Formula; \\ \frac{y}{z}=x \\ \\ Therefore, \\ \\ \frac{15\ miles}{30\ minutes}=x \\ \\ \boxed{7.5\ miles=x}

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2014-11-21T00:22:35+08:00
Let 'S' be the distance from starting point up to the Finish line.
      't' be the time to finished the race.
      'v' be the velocity
      'X' be the distance of Barry from the finish line When Sean finished the race.
Considering Sean:
  v=S/t
  t =S/v
  t = 30/20
  t = 3/2 hr

Considering Berry :
  v =(30-X)/t         
but the time takes of Sean to finish the race is equal to the time of Berry to finish the race.So,
   vt = (30-X)
   (15)(3/2) = (30-X)
    X = 7.5 miles           (ans.)


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