Question

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 1

Answer: $8\ miles$

Step-by-step 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:

$t_1=20\ min=\frac{(20\ min)(1\ h)}{60\ min}=\frac{1}{3}\ h\\\\V_1=V_2+8\ mph\\\\t_2=30\ min=\frac{(30\ min)(1\ h)}{60\ min}=\frac{1}{2}\ h$

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

$V_1*t_1=V_2*t_2\\\\(V_2+8)(\frac{1}{3})=(V_2)(\frac{1}{2})$

Solving for $V_2$, we get:

$2(V_2+8)(\frac{1}{3})=3(V_2)\\\\2V_2+16=3V_2\\\\V_2=16\ mph$

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

$d=(16\ mph)(\frac{1}{2}\ h)\\\\d=8\ miles$