Question

12.4 submarines

1. a submarine is descending to examine the seafloor 2,100 feet below the surface. it takes the submarine 2 hours to make this descent. write an equation to represent the relationship between the submarines elevation and time.

1. another submarines descent can be represented as $y = -240x$, where $y$ is the elevation and $x$ is time in hours. how long will it take this submarine to make the descent?

Explanation:

Step1: Find descent rate (Q1)

The submarine descends 2100 feet in 2 hours, so the rate is $\frac{-2100}{2} = -1050$ feet/hour. Elevation starts at 0, so the equation follows $y = mx + b$ where $b=0$.

Step2: Write elevation-time equation (Q1)

$y = -1050x$, where $y$ = elevation (ft), $x$ = time (hrs).

Step3: Set elevation to -2100 (Q2)

Substitute $y = -2100$ into $y = -240x$.

Step4: Solve for time $x$ (Q2)

$x = \frac{-2100}{-240} = 8.75$

Answer:

1. $y = -1050x$ (where $y$ is the submarine's elevation in feet, $x$ is time in hours)
2. 8.75 hours