At the beginning of a walk, roberto and juanita are 7.77.7 miles apart. if they leave at the same time and walk in the same direction, roberto overtakes juanita in 11 hours. if they walk towards each other, they meet in 1 hour. what are their speeds

Roberto overtakes Juanita at the rate of (7.7 mi)/(11 h) = 0.7 mi/h. This is the difference in their speeds. The sum of their speeds is (7.7 mi)/1 h) = 7.7 mi/h.

Roberto walks at the rate (7.7 + 0.7)/2 = 4.2 mi/h.
Juanita walks at the rate 4.2 - 0.7 = 3.5 mi/h.


In a "sum and diference" problem, one solution is half the total of the sum and difference. If we let R and J be the respective speeds of Roberto and Juanita, we have
  R + J = total speed
  R - J = difference speed
Adding these two equations, we have
  2R = (total speed + difference speed)
  R = (total speed + difference speed)2 . . . . . as computed above