Question

starting at sea level, a submarine descended at a constant rate to a depth of $-\frac{3}{4}$ mile relative to sea level in $\frac{5}{8}$ minutes. the submarine continues to descend at the same rate. what is the submarines depth relative to sea level after the first minute? enter your answer as a simplified mixed number in the box mile

Explanation:

Step1: Find the rate of descent

We know that rate = distance/time. The distance is $-\frac{3}{4}$ mile and the time is $\frac{5}{8}$ minutes. So the rate $r$ is $r=\frac{-\frac{3}{4}}{\frac{5}{8}}$.

Step2: Simplify the rate - calculation

Using the rule of dividing fractions $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$, we have $r =-\frac{3}{4}\times\frac{8}{5}=-\frac{3\times8}{4\times5}=-\frac{24}{20}=-\frac{6}{5}$ miles per minute.

Step3: Find the depth after 1 minute

Since the rate is $-\frac{6}{5}$ miles per minute and time $t = 1$ minute, the depth $d$ is $d=r\times t$. Substituting $r=-\frac{6}{5}$ and $t = 1$ gives $d=-\frac{6}{5}=- 1\frac{1}{5}$ miles.

Answer:

$-1\frac{1}{5}$