Question

match the scenarios to the equations. a whale was diving at a rate of 5 meters per second. how long will it take for the whale to get from the surface of the ocean to an elevation of -15 meters at that rate? a swimmer dove below the surface of the ocean. after 5 minutes, she was 15 meters below the surface. at what rate was she diving? -5m = -15 5m = -15

Explanation:

Step1: Analyze First Scenario

The whale's diving rate is 5 meters per second (negative since it's below surface, so -5 m/s). Let time be \( m \) seconds. Distance = rate × time, so \(-5m = -15\) (distance to -15 meters).

Step2: Analyze Second Scenario

The swimmer dives for 5 minutes (time \( m = 5 \)), ends at -15 meters. Let rate be \( 5 \) (wait, no—rate is \( r \), but equation is \( 5m = -15 \) where \( m \) is time? Wait, first scenario: rate is -5 m/s, time \( m \), distance -15: \(-5m = -15\). Second scenario: time 5 minutes (so \( m = 5 \)), rate \( r \), distance -15: \( r \times 5 = -15 \) → \( 5m = -15 \) (let \( m \) be time here? Wait, maybe variables: first scenario: rate -5, time \( m \), distance -15: \(-5m = -15\). Second scenario: time 5, rate \( m \)? No, equations: \(-5m = -15\) matches first scenario (rate -5, time \( m \), distance -15). \( 5m = -15 \) matches second scenario (time 5, rate \( m \)? Wait, no—second scenario: after 5 minutes (time = 5), depth -15. So rate \( r \), \( r \times 5 = -15 \) → \( 5r = -15 \), but equation is \( 5m = -15 \), so \( m \) is rate here? Maybe. So first scenario: whale's rate is -5, time \( m \), so \(-5m = -15\). Second scenario: time 5, rate \( m \), so \( 5m = -15 \).

Step3: Match Scenarios to Equations

First scenario (whale): rate -5, time \( m \), distance -15 → \(-5m = -15\). Second scenario (swimmer): time 5, rate \( m \), distance -15 → \( 5m = -15 \).

Answer:

• "A whale was diving at a rate of 5 meters per second. How long will it take for the whale to get from the surface of the ocean to an elevation of -15 meters at that rate?" matches \(\boldsymbol{-5m = -15}\)
• "A swimmer dove below the surface of the ocean. After 5 minutes, she was 15 meters below the surface. At what rate was she diving?" matches \(\boldsymbol{5m = -15}\)