According to the statement, to find the distance between Omar's home and the mountains we need to use a system of equations.
Taking x as the average rate and a y as the distance, we know that the distance equals the average rate times the hours that the trip took.
In this case, in the way to the mountains the distance y is x times 6 which was the number of hours that the trip took.
[tex]y=6x[/tex]In the way home, the distance y is x plus 22 (because the average rate was 22 faster) times 4 which was the number of hours that the trip took.
[tex]y=4(x+22)[/tex]Make both expressions equal and find the value of x:
[tex]\begin{gathered} 6x=4(x+22) \\ 6x=4x+88 \\ 6x-4x=88 \\ 2x=88 \\ x=\frac{88}{2} \\ x=44 \end{gathered}[/tex]The average rate was 44 in the trip to the mountains, use this value to find the distance:
[tex]\begin{gathered} y=6x \\ y=6(44) \\ y=264 \end{gathered}[/tex]Omar lives 264 miles far way from the mountains.
