Question

Michael drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when michael drove home, there was no traffic and the trip only took 4 hours. if his average rate was 27 miles per hour faster on the trip home, how far away does Michael live from the mountains ?do not do any rounding

Answer 1

Given: The information below

`\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}`

To Determine: How far away Micheal live from the mountains

The rate is

`r_{\text{ate}}=(dis\tan ce(miles))/(time(hours))`
`\begin{gathered} r_{\text{ate during heavy traffic}}=(d)/(7) \\ r_{\text{ate during no traffic}}=(d)/(4) \\ d=\text{distance from home to the mountains} \end{gathered}`
`\begin{gathered} (d)/(4)=(d)/(7)+27_{} \\ (d)/(4)-(d)/(7)=27 \\ (7d-4d)/(28)=27 \\ (3d)/(28)=27 \\ 3d=27*28 \\ (3d)/(3)=(27*28)/(3) \\ d=9*28 \\ d=252 \end{gathered}`

Hence, the Micheal distance from the mountain is 252 miles