21.8k views
0 votes
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

1 Answer

3 votes

Answer:
8\ miles

Explanation:

We know that the formula for the distance is:


d=V*t

Where "V" is speed and "t" is time.

Let be:


t_1: time of her trip from her home to the library.


t_2: time of her trip from the library to her home.


V_1: speed on her trip from her home to the library.


V_2: speed on her trip from the library to her home

We can identify that:


t_1=20\ min=((20\ min)(1\ h))/(60\ min)=(1)/(3)\ h\\\\V_1=V_2+8\ mph\\\\t_2=30\ min=((30\ min)(1\ h))/(60\ min)=(1)/(2)\ h

Since the distance she rode on the both trips are equal:


V_1*t_1=V_2*t_2\\\\(V_2+8)((1)/(3))=(V_2)((1)/(2))

Solving for
V_2, we get:


2(V_2+8)((1)/(3))=3(V_2)\\\\2V_2+16=3V_2\\\\V_2=16\ mph

Therefore, the distance for her home to the library is:


d=(16\ mph)((1)/(2)\ h)\\\\d=8\ miles

User Leepowers
by
7.3k points