Question

10.) a scuba diver is currently at an elevation of 45.5 meters below sea level. she begins to ascend toward the surface at a constant rate of 2.5 meters per minute. after several minutes, she pauses her ascent at an elevation of -18.25 meters to perform a safety stop. how many minutes (m) did she spend ascending before she reached the safety stop? write and solve an equation.

Explanation:

Step1: Define the variables and equation

Let \( m \) be the number of minutes spent ascending. The initial elevation is -45.5 meters (below sea level), and she ascends at 2.5 meters per minute, so the elevation after \( m \) minutes is \( -45.5 + 2.5m \). This equals -18.25 meters when she stops. So the equation is:
\( -45.5 + 2.5m = -18.25 \)

Step2: Solve for \( m \)

Add 45.5 to both sides:
\( 2.5m = -18.25 + 45.5 \)
\( 2.5m = 27.25 \)

Divide both sides by 2.5:
\( m = \frac{27.25}{2.5} \)
\( m = 10.9 \)

Answer:

The diver spent 10.9 minutes ascending. The equation is \( -45.5 + 2.5m = -18.25 \) and the solution is \( m = 10.9 \).