Question

Tammy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Tammy drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Tammy live from the mountains?

Answer 1

`\begin{equation*} 315\text{ }miles \end{equation*}`

Step-by-step explanation

Let her average rate on the trip to the mountains be x miles per hour.

This implies that her average rate on her way home was (x + 18) miles per hour.

The distance traveled can be found using the formula for speed(average rate):

`\begin{gathered} speed=(distance)/(time) \\ \\ distance=speed*time \end{gathered}`

Therefore, on her way to the mountains:

`d=x*7`

And on her way home:

`d=(x+18)*5`

Since the distance is the same for both trips, equate the two equations:

`\begin{gathered} x*7=(x+18)*5 \\ \\ 7x=5x+90 \end{gathered}`

Solve for x in the equation:

`\begin{gathered} 7x-5x=90 \\ \\ 2x=90 \\ \\ x=(90)/(2) \\ \\ x=45\text{ mph} \end{gathered}`

Substitute the value of x into the equation for distance to find the distance:

`\begin{gathered} d=45*7 \\ \\ d=315\text{ }miles \end{gathered}`

That is the distance from the mountains to where Tammy lives.