Question 448811: At the beginning of a walk Roberto and Juanita are 7.7 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?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Roberto x------ speed
Jaunita ------------y speed
x+2y=1 .............1
1x-1y=0.7.............2
Eliminate y
multiply (1)by 1
Multiply (2) by -2
x+2y= 1
-2x+2y=-1.4
Add the two equations
-1x=-0.4
/-1
x=0.40
plug value of x in (1)
1x+2y=1
0.4+2y=1
2y=1-0.4
2y=0.6
y=0.30
Answer by ikleyn(53427)  (Show Source):
You can put this solution on YOUR website! .
At the beginning of a walk Roberto and Juanita are 7.7 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?
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The solution in the post by @mananth is INCORRECT.
I came to bring a correct solution.
Let R be the Roberto speed in miles per hour, and
let J be the Juanita speed.
Then in the first case the approaching speed is
R - J =  = 0.7 mph.
In the second case, the approaching speed is
R + J =  = 7.7.
Add equations and get
2R = 0.7 + 7.7 = 8.4, R = 8.4/2 = 4.2 mph.
Subtract equations and get
2J = 7.7 - 0.7 = 7, J = 7/2 = 3.5 mph.
At this point, the problem is solved completely.
ANSWER. Roberto speed is 4.2 mph. Juanita speed is 3.5 mph.
That's all.
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