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A straight highway is 100 miles long, and each mile is marked by a milepost numbered from 0 to 100. A rest area is going to be built along the highway exactly 6 miles away from milepost 57. If m is the milepost number of the rest area, which of the following equations represents the possible locations for the rest area?A.|m - 6| = 57B.|57 - m| = 6C.|57 + m| = 6D.|m + 6| = 57

Question

A straight highway is 100 miles long, and each mile is marked by a milepost numbered from 0 to 100. A rest area is going to be built along the highway exactly 6 miles away from milepost 57. If m is the milepost number of the rest area, which of the following equations represents the possible locations for the rest area?A.|m - 6| = 57B.|57 - m| = 6C.|57 + m| = 6D.|m + 6| = 57

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Solution

The correct equation that represents the possible locations for the rest area is B. |57 - m| = 6.

Here's why:

The rest area is going to be built along the highway exactly 6 miles away from milepost 57. This means the rest area could be 6 miles before milepost 57 or 6 miles after milepost 57.

If the rest area is 6 miles before milepost 57, then the milepost number of the rest area, m, would be 57 - 6 = 51.

If the rest area is 6 miles after milepost 57, then the milepost number of the rest area, m, would be 57 + 6 = 63.

So, the rest area could be at milepost 51 or milepost 63.

The absolute value equation |57 - m| = 6 captures both of these possibilities. If m = 51, then |57 - 51| = 6, which is true. If m = 63, then |57 - 63| = 6, which is also true.

Therefore, the correct equation is B. |57 - m| = 6.

This problem has been solved

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