Question

Omar drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. WhenOmar drove home, there was no traffic and the trip only took 4 hours. If his average rate was 22 miles per hour faster onthe trip home, how far away does Omar live from the mountains?Do not do any rounding.

Answer 1

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.

`y=6x`

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.

`y=4(x+22)`

Make both expressions equal and find the value of x:

`\begin{gathered} 6x=4(x+22) \\ 6x=4x+88 \\ 6x-4x=88 \\ 2x=88 \\ x=(88)/(2) \\ x=44 \end{gathered}`

The average rate was 44 in the trip to the mountains, use this value to find the distance:

`\begin{gathered} y=6x \\ y=6(44) \\ y=264 \end{gathered}`

Omar lives 264 miles far way from the mountains.