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?

1 Answer
John D.
Feb 9, 2018

The expression for position in relation to time is:

#p = -7/2t#

After 3 minutes, the diver is at #21/2#, or #10.5# meters below the surface.

Explanation:

In this case, #-7/2 "m"/"min"# is our #"speed"#, or #"rate of change"#.

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

#color(limegreen)"position " = color(red)" original position " + color(blue)" speed" xx "time"#

Let's call our new position #color(limegreen)p#. The problem tells us that our original position is #color(red)0# (since the diver starts at the surface, which is 0 meters below the surface), and that the speed of the diver is #color(blue)(-7/2) "m"/"min" #.

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

#color(limegreen)p = color(red)0 + color(blue)((-7/2))t#

#color(limegreen)p = color(blue)(-7/2)t#

Now, to solve for #color(limegreen)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 #color(limegreen)p#.

#color(limegreen)p = color(blue)(-7/2)(3)#

#color(limegreen)p = -21/2#

#color(limegreen)p = -10.5#

So, after 3 minutes, the diver is at #-21/2#, or #-10.5# meters.

This means that he is #21/2#, or #10.5# meters below the surface of the water.

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