Given: The information below
[tex]\begin{gathered} T_{he\text{ time trip during heavy traffic}}=7hours \\ T_{he\text{ time trip during no traffic}}=4hours \\ T_{he\text{ average rate}}=27miles\text{ per hour} \end{gathered}[/tex]To Determine: How far away Micheal live from the mountains
The rate is
[tex]r_{\text{ate}}=\frac{dis\tan ce(miles)}{time(hours)}[/tex][tex]\begin{gathered} r_{\text{ate during heavy traffic}}=\frac{d}{7} \\ r_{\text{ate during no traffic}}=\frac{d}{4} \\ d=\text{distance from home to the mountains} \end{gathered}[/tex][tex]\begin{gathered} \frac{d}{4}=\frac{d}{7}+27_{} \\ \frac{d}{4}-\frac{d}{7}=27 \\ \frac{7d-4d}{28}=27 \\ \frac{3d}{28}=27 \\ 3d=27\times28 \\ \frac{3d}{3}=\frac{27\times28}{3} \\ d=9\times28 \\ d=252 \end{gathered}[/tex]Hence, the Micheal distance from the mountain is 252 miles
