becky Anderson can ride her bike to the university library in 20 minutes the trip home which is uphill takes 30 minutes if a rate is 8 mph faster on her trip there then her trip home how far does she live from the library

Answer: [tex]8\ miles[/tex]Step-by-step explanation: We know that the formula for the distance is: [tex]d=V*t[/tex] Where "V" is speed and "t" is time. Let be: [tex]t_1[/tex]: time of her trip from her home to the library. [tex]t_2[/tex]: time of her trip from the library to her home. [tex]V_1[/tex]: speed  on her trip from her home to the library. [tex]V_2[/tex]: speed on her trip from the library to her home   We can identify that: [tex]t_1=20\ min=\frac{(20\ min)(1\ h)}{60\ min}=\frac{1}{3}\ h\\\\V_1=V_2+8\ mph\\\\t_2=30\ min=\frac{(30\ min)(1\ h)}{60\ min}=\frac{1}{2}\ h[/tex] Since the distance she rode on the both trips are equal: [tex]V_1*t_1=V_2*t_2\\\\(V_2+8)(\frac{1}{3})=(V_2)(\frac{1}{2})[/tex] Solving for [tex]V_2[/tex], we get: [tex]2(V_2+8)(\frac{1}{3})=3(V_2)\\\\2V_2+16=3V_2\\\\V_2=16\ mph[/tex] Therefore, the distance for her home to the library is: [tex]d=(16\ mph)(\frac{1}{2}\ h)\\\\d=8\ miles[/tex]