```Question 380564
At the beginning of a walk, Roberto and Juanita are 6.6 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?
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Draw the two pictures.

Walk toward one another DATA:
Let Roberto distance be "x"
Then Roberto time = 1 hr
And Roberto rate = x mph
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Juanita distance is "6.6-x"
Juanita time = 1 hr
Juanita rate = (6.6-x) mph
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Same Direction DATA:
Roberto distance = (6.6+y)miles
Roberto time = 11 hrs
Roberto rate = x
Roberto equation:
distance = distance:
11x = 6.6+y
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Juanita distance = y miles
Juanita rate = (6.6-x) mph
Juanita time = 11 hrs
Juanita equation:
distance = distance
y = 11(6.6-x)
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Solve the system:
11x - y = 6.6
-11x -y = -72.6
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Subtract to solve for "x"
22x = 79.2
x = 3.6 mph (Roberto's walking rate)
6.6-x = 3 mph (Juanita's walking rate)
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Cheers,
Stan H.```