This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
 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}

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:
  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.)