Respuesta :
You know that:
- Last weekend his trip took 10 hours when he drove to the mountains.
- When he drove home, the trip took 7 hours.
- His average rate was 18 miles per hour faster on the trip home.
By definition, the distance can be calculated with this formula:
[tex]d=rt[/tex]Where "d" is distance, "r" is rate, and "t" is time.
Then, you can set up the following equation to represent his trip to the mountains ("d" is in miles):
[tex]d=10r[/tex]And you can set up the following equation to represent his trip home ("d" is in miles):
[tex]d=7(r+18)[/tex]To find the value of "r", you need to make both equations equal to each other and solve for "r". Then, you get:
[tex]\begin{gathered} 10r=7(r+18) \\ 10r=7r+126 \\ 10r-7r=126 \\ \\ r=\frac{126}{3} \\ \\ r=42 \end{gathered}[/tex]Knowing the value of "r", you can substitute it into the second equation:
[tex]\begin{gathered} d=7\mleft(r+18\mright) \\ d=(7)\mleft(42+18\mright) \end{gathered}[/tex]Finally, evaluating, you get (Remember that "d" is in miles)
[tex]\begin{gathered} d=(7)(60) \\ d=420 \end{gathered}[/tex]Therefore, the answer is:
[tex]420\text{ }miles[/tex]