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Letha walked s feet away at y feet per minute and arrived at the library 10 minutes late. How fast should she have walked to arrived on time?
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Not sure this is best approach
not sure I understand the description correctly but,..
y, speed as done
y+k, some wanted higher speed
s, distance to get to library
            SPEED    TIME    DISTANCE
LATE           y      s/y       s
ON TIME       y+k     s/(y+k)   s
DIFFERENCE             10
WANT TO KNOW 
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Solving for ,
--------the normal speed