Question

1. a scuba diver is diving at a constant rate when her team on the surface requests a status update. she looks at her watch which says her elevation is 18 feet below sea level. 8 seconds later, her elevation is 20 feet below sea level.

a. at what rate is her elevation changing? use a signed number, and include the unit of measurement in your answer.
b. how many more seconds until she reaches her goal depth of 50 feet? explain or show your reasoning.
c. how many seconds before her team requested an update was the diver at the surface of the water? explain or show your reasoning.

Explanation:

Step1: Calculate elevation change

$\text{Change in elevation} = 20 - 18 = 2$ feet (negative, since it's deeper)

Step2: Find rate of change

$\text{Rate} = \frac{\text{Change in elevation}}{\text{Time}} = \frac{-2}{8} = -0.25$ feet/second
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Step3: Find remaining depth for part b

$\text{Remaining depth} = 50 - 20 = 30$ feet

Step4: Calculate time for part b

$\text{Time} = \frac{\text{Remaining depth}}{\text{Absolute value of rate}} = \frac{30}{0.25} = 120$ seconds
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Step5: Find depth from surface for part c

$\text{Depth at update} = 18$ feet

Step6: Calculate time for part c

$\text{Time} = \frac{\text{Depth from surface}}{\text{Absolute value of rate}} = \frac{18}{0.25} = 72$ seconds

Answer:

a. $-0.25$ feet per second
b. 120 seconds
c. 72 seconds