Question 265733
Let the speed of Smith = x mph
Then, the speed of Jones = x+5
Given, Smith bicycled 45 miles going east from Dursango, and Jones bicycled 70 miles. 
Time = Distance/speed.
Time taken by Smith = 45/x
Time taken by Jones = 70/(x+5)
Gien, Jone's trip took one-half hour longerthan smith's. 
      70/(x+5) = 45/x +  1/2
      70/(x+5) = 45/x+1/2
      70/(x+5) = (90+x)/2x
      140x = (90+x)(x+5)
      140x = 90x+450+x^2+5x
         0 = x^2-45x+450
      x^2-45x+450 = 0
      (x-30)(x-15) = 0
       x = 30 or 15
Therefore the speed of Smith = 30 mph and Then, the speed of Jones =35 mph
or the speed of Smith = 15 mph and the speed of Jones = 20 mph