Hi

first man travels 10 miles per hour faster than the second man

Let x and (x+10mph)represent the speed of the slower and faster man respectively

Question states***  NOte: D = r*t  OR   D/r = t

500/x - 500/(x+10)  = 2.5

Solving for x

500(x+10)-500x = 2.5x(x+10)

   2.5x^2 + 25x -5000 = 0

      x^2 + 10x -2000= 0

factoring

(x + 50)(x-40) = 0 Note:SUM of the inner product(50x) and the outer product(-40x) = 10x

(x + 50)= 0  |tossing out negative solution for time

(x - 40) = 0  x = 40mph, speed of slower man.  Faster man's speed is 50mph



CHECKING our Answer***

500mi/40mph - 500mi/50mph  = 12.5hr  - 10hr = 2.5hr 

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