# A deep sea diver changes his position relative to the surface of the water by -7/2 meters per minute. How do you write and evaluate an expression to show his position after 3 minutes if he starts at the surface of the water?

Feb 9, 2018

The expression for position in relation to time is:

$p = - \frac{7}{2} t$

After 3 minutes, the diver is at $\frac{21}{2}$, or $10.5$ meters below the surface.

#### Explanation:

In this case, $- \frac{7}{2} \text{m"/"min}$ is our $\text{speed}$, or $\text{rate of change}$.

When we're dealing with position and time, we use the following formula:

$\textcolor{\lim e g r e e n}{\text{position " = color(red)" original position " + color(blue)" speed" xx "time}}$

Let's call our new position $\textcolor{\lim e g r e e n}{p}$. The problem tells us that our original position is $\textcolor{red}{0}$ (since the diver starts at the surface, which is 0 meters below the surface), and that the speed of the diver is $\textcolor{b l u e}{- \frac{7}{2}} \text{m"/"min}$.

Let's also call our time variable $t$. Therefore, our equation becomes:

$\textcolor{\lim e g r e e n}{p} = \textcolor{red}{0} + \textcolor{b l u e}{\left(- \frac{7}{2}\right)} t$

$\textcolor{\lim e g r e e n}{p} = \textcolor{b l u e}{- \frac{7}{2}} t$

Now, to solve for $\textcolor{\lim e g r e e n}{p}$. The problem tells us that we need to find the diver's position after $3$ minutes. So, let's plug in $3$ for $t$, and simplify the expression to get our value for $\textcolor{\lim e g r e e n}{p}$.

$\textcolor{\lim e g r e e n}{p} = \textcolor{b l u e}{- \frac{7}{2}} \left(3\right)$

$\textcolor{\lim e g r e e n}{p} = - \frac{21}{2}$

$\textcolor{\lim e g r e e n}{p} = - 10.5$

So, after 3 minutes, the diver is at $- \frac{21}{2}$, or $- 10.5$ meters.

This means that he is $\frac{21}{2}$, or $10.5$ meters below the surface of the water.