A straight highway is 100 miles long. Each mile is marked by a milepost numbered from 0 to 100. Where is the best place to build a rest area along the highway if it should be exactly 7 miles away from milepost 58?
Solution:
To determine the optimal location for the rest area, we can use the following steps:
Milepost Number of the Rest Area
The distance between the rest area and milepost 58 can be represented by the equation:
|M - 58| = 7
Where M is the milepost number of the rest area. Solving this equation gives two possible values for M:
M = 51 or M = 65
Rest Area Location
This means that the rest area can be built either 7 miles before milepost 58 or 7 miles after milepost 58. Therefore, the possible locations for the rest area are milepost 51 and milepost 65.
Distance from Mileposts
The distance from milepost 51 to the rest area is 7 miles. Similarly, the distance from milepost 65 to the rest area is also 7 miles. This indicates that the rest area is equidistant from mileposts 51 and 65.
Optimal Location
Based on the analysis above, the optimal location for the rest area is in the middle of the highway. Specifically, it should be located at:
Milepost 58 ± 7 miles
This ensures that the rest area is easily accessible to drivers traveling in both directions, providing maximum convenience and safety.
FAQ about the Highway Rest Area
Where will the rest area be built?
The rest area will be built 7 miles away from milepost 58, at either milepost 51 or milepost 65.
Why are there two possible locations for the rest area?
The equation |M – 58|= 7 has two solutions, M = 51 and M = 65. This means that the rest area can be built either 7 miles before milepost 58 or 7 miles after milepost 58.
Which milepost is the rest area closest to?
The rest area is equidistant from mileposts 51 and 65, so it is closest to both of them.
How far is the rest area from the beginning and end of the highway?
The rest area is 51 miles from the beginning of the highway and 49 miles from the end of the highway.
