Question 416339
Let s = her speed on the way to the library in mph
Her speed on the way from the library = s - 8
Her travel times in hours are 
20 min/60 min = 1/3 hr (to) and 30/60 = 1/2 hr (from) library
The distance from home to library = s*(1/3)
The distance from library to home = (s-8)*(1/2)
Since these two distances are equal, we have {{{s/3 = (s-8)/2}}}
Solving for s gives {{{(-1/6)s = -4}}} -> s = 24 mph
Therefore, the distance to the library = 24 mph*(1/3 hr) = 8 miles