Question

1. challenger deep is the deepest known point in the ocean, at 35,814 feet below sea level. in 1960, jacques piccard and don walsh rode down in the trieste and became the first people to visit the challenger deep.

a. if sea level is represented by 0 feet, explain how you can represent the depth of a submarine descending from sea level to the bottom of challenger deep.
b. trieste’s descent was a change in depth of -3 feet per second. we can use the relationship $y = -3x$ to model this, where $y$ is the depth (in feet) and $x$ is the time (in seconds). using this model, how much time would the trieste take to reach the bottom?

Explanation:

Step1: Part a: Define depth representation

Since sea level is 0, depths below it are negative values. The depth of the submarine can be represented as a negative number ranging from $0$ (at sea level) to $-35,814$ feet (at the bottom of Challenger Deep).

Step2: Part b: Set target depth

The bottom depth $y = -35,814$ feet. Substitute into $y=-3x$.
$$-35,814 = -3x$$

Step3: Part b: Solve for time $x$

Divide both sides by $-3$ to isolate $x$.
$$x = \frac{-35,814}{-3}$$
$$x = 11,938$$

Answer:

a. The submarine's depth is represented by a negative number that starts at 0 (sea level) and decreases to -35,814 feet at the bottom of Challenger Deep, as negative values denote positions below the 0 reference point (sea level).
b. 11,938 seconds