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`

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`