A submarine descends from sea level to the entrance of an underwater cave. The elevation of the entrance is -120 feet. The rate of change in the submarine's elevation is no greater than -12 feet per second. Can the submarine reach the entrance to the cave in less than 10 seconds?

**Write as an inequality
THANK YOU!!

http://www.jiskha.com/display.cgi?id=1445809291

To determine whether the submarine can reach the entrance of the cave in less than 10 seconds, we need to compare the time it takes with the given rate of change in elevation.

Let's define the time taken as "t" and the elevation of the entrance as "-120". The rate of change of the submarine's elevation is "-12" feet per second.

From the given information, we can write the equation:

Rate of Change × Time + Initial Elevation = Final Elevation

Using the variables defined, the equation becomes:

-12t + 0 ≥ -120

We multiply the -12 by t because the rate of change is given per second, and the equation checks whether the submarine's elevation can reach the entrance in less than 10 seconds.

To find out if the submarine can reach the entrance of the cave in less than 10 seconds, we need to solve for t.

-12t + 0 ≥ -120

Rearranging the equation, we get:

-12t ≥ -120

To isolate t, we divide both sides by -12. However, since we are dividing by a negative number, the inequality sign should be reversed:

t ≤ (-120)/(-12)

Simplifying the expression, we have:

t ≤ 10

Therefore, the submarine can reach the entrance of the cave in less than or equal to 10 seconds, as the submarine's rate of change in elevation is no greater than -12 feet per second.