SOLUTION: At the beginning of a walk, Roberto and Juanita are 4.4 miles apart. If they leave at the Same time and walk in the Same direction Roberto overtakes Juanita in 11hrs. If they walk

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Question 710809: At the beginning of a walk, Roberto and Juanita are 4.4 miles apart. If they leave at the Same time and walk in the Same direction Roberto overtakes Juanita in 11hrs. If they walk towards each other, they meet in 1he. What are their speeds? I would like help with what formulation to use so I can plug in my numbers....please
ThAnk you
Laura
thewrighttoad08@gmail.com
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In order for Roberto to overtake Juanita, he has to be the faster walker.
Walking in the same direction:
Let +d+ = the distance Roberto travels until he catches Juanita
+d+-+4.4+ = the distance Juanita travels when Roberto catches her
Let +r+ = Roberto's speed
Let +s+ = Juanita's speed
------------------------
Roberto's equation:
(1) +d+=+r%2A11+
Juanita's equation:
(2) +d+-+4.4+=+s%2A11+
------------------
Walking towards each other:
They approach each other at the sum of their speeds, and
together, they cover +4.4+ mi
+4.4+=+%28+r+%2B+s+%29%2A1+
(3) +r+%2B+s+=+4.4+
-----------------
Substitute (1) into (2)
(2) +11r+-+4.4+=+s%2A11+
(2) +11r+-+11s+=+4.4+
(2) +r+-+s+=+.4+
---------------
Add equations (2) and (3)
(3) +r+%2B+s+=+4.4+
(2) +r+-+s+=+.4+
+2r+=+4.8+
+r+=+2.4+
and, since
(3) +r+%2B+s+=+4.4+
(3) +2.4+%2B+s+=+4.4+
(3) +s+=+2+
Roberto's speed is 2.4 mi/hr
Juanita's speed is 2 mi/hr