Question

A cave explorer is at an elevation of −38​ feet. The explorer starts moving at a rate of −12 feet per minute. The relationship between the explorer's elevation y, and her rate of decrease x, can be represented be the inequality 7 = -12x -38.

Solve the inequality to determine how many minutes it will take the explorer to reach an elevation deeper than -200 feet.

-200
`\geq \\` -12x - 38

Answer 1

To solve this inequality, we need to isolate the x-variable on one side of the equation. To do this, we can add 38 to both sides of the equation to get the following:

-200 - 12x - 38 = 38

-200 - 12x = 76

Next, we can divide both sides of the equation by -12 to get the following:

-200 - 12x = 76

x = -17

Finally, we can use the value of x to determine how long it will take the explorer to reach an elevation deeper than -200 feet. Since the explorer moves at a rate of -12 feet per minute, it will take her 17 minutes to reach this depth.