Question

1. draw conclusions 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 less than -12 feet per second. can the submarine reach the entrance to the cave in less than 10 seconds? explain.

Explanation:

Step1: Define variables and inequality

Let $r$ = rate of elevation change (ft/s), $t$ = time (s). We know $r < -12$, and total elevation change needed is $-120$ ft. The relationship is $r \times t = -120$, so $t = \frac{-120}{r}$.

Step2: Substitute the rate constraint

Since $r < -12$, take reciprocals (reverse inequality): $\frac{1}{r} > -\frac{1}{12}$. Multiply both sides by $-120$ (reverse inequality again):
$$t = \frac{-120}{r} < \frac{-120}{-12}$$

Step3: Calculate the threshold time

$$\frac{-120}{-12} = 10$$
So $t < 10$.

Answer:

Yes, the submarine can reach the cave entrance in less than 10 seconds. Since its descent rate is faster than -12 feet per second (more negative), the time required to descend 120 feet will be less than the 10 seconds it would take at exactly -12 feet per second.