Question

During a scuba dive, Lainey descended to a point 29 feet below the ocean surface. She continued her descent at a rate of 29 feet per minute. Enter an inequality you could solve to find the number of minutes she can continue to descend if she does not want to reach a point more than 81 feet below the ocean surface. Use t to represent the variable for the minutes Lainey can continue to descend.

Answer 1

Her initial position was:

-29ft

Where we use the minus sign because this is below the ocean's surface.

Now we also know that she keeps descending at a rate of -29ft per minute, then if she keeps descending for t minutes, her position will be:

P(x) = -29ft - 29ft/min*t

Now, we also know that she does not want to descend more than 81ft below the ocean's surface, then we have the inequality:

P(x) ≥ -81ft

-29ft - 29ft/min*t ≥ -81ft

Now let's isolate t in one side:

- 29ft/min*t ≥ -81ft + 29ft = -52 ft

- 29ft/min*t ≥-52 ft

t ≤ -52ft/(- 29ft/min) = 1.79 min

Then the maximum amount of time that she can keep descending is 1.79 minutes.