Question 1118486
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Let x be Libby's regular speed (in the first scenario), in miles per hour.


Then the distance to work is  distance = d = time*speed = 1 hour * x miles per hour = x miles.


This distance is equal to time*speed in the second scenario:


d = 0.75*(x+10)  miles.    (0.75 of an hour = 3/4 of an hour.)


Distance is the same, which gives you an equation


x = 0.75*(x+10),


Simplify and solve for x:


x = 0.75x + 7.5,

x - 0.75x = 7.5

0.25x = 7.5  ====>  x = {{{7.5/0.25}}} = 30 miles per hour.


<U>Answer</U>.  The distance to work is 30 miles.
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The solution by @addingup is incorrect.