Question

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

Answer 1

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.


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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