Question

sam and sonya are scuba diving. sam is at an elevation of -42 feet, and she is descending at a rate of 10 feet per minute. sonya is at an elevation of -12 feet and she is descending at a rate of 14 feet each minute. the variable t represents the time in minutes. after how many minutes will sam and sonya be at the same elevation? at what elevation will they be at that time?
use the expressions to help you solve. after how many minutes will sam and sonya be at the same elevation? solve on paper, then enter your answer on zearn.
sams elevation after t minutes: -42 + (-10t)
sonyas elevation after t minutes: -12 + (-14t)
sam and sonya will be at the same elevation after
minutes.

Explanation:

Step1: Set elevations equal

$-42 + (-10t) = -12 + (-14t)$

Step2: Simplify both sides

$-42 -10t = -12 -14t$

Step3: Isolate t terms

$-10t +14t = -12 +42$

Step4: Calculate t

$4t = 30$
$t = \frac{30}{4} = 7.5$

Step5: Find shared elevation

Substitute $t=7.5$ into Sam's formula:
$-42 + (-10 \times 7.5) = -42 -75 = -117$

Answer:

Sam and Sonya will be at the same elevation after 7.5 minutes, at an elevation of -117 feet.