Hi,         

Let x and (x+10)represent the speed hiking and biking respectively

D = r*t Or D/r = t. Total time for the trip was 5 hours.

Question States***

12/(x+10) + 8/x = 5hr Multiplying each term by x(x+10) so as all denominators = 1

 12x + 8(x+10) =5x(x+10)

Solving for x

  12x + 8x + 80 = 5x^2 + 50x

  5x^2 + 30x - 80 = 0

  5(x^2 + 6x - 16) = 0

(x + 8)(x - 2) = 0 Note:SUM of the inner product(8x) and the outer product(-2x) =6x

(x + 8= 0

  x = -8  Tossing out negative answer

(x - 2) = 0

  x = 2mph, speed hiking.  Speed biking was 12mph.   (2mph + 10mph)



CHECKING our Answer***

 12mi/12mph + 8mi/2mph = 1hr + 4hr = 5hr 

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