Final answer:
The correct inequality to represent the scuba diver's situation is 80 - 1.2t ≥ 15. After solving, we find that the diver can stay underwater for less than or equal to 54 minutes, which corresponds to answer choice a.
Step-by-step explanation:
The student's question is asking us to determine how long a scuba diver can stay underwater with an 80 cubic foot tank of air given that they breathe at a rate of 1.2 cubic feet per minute and must surface when the tank reaches at least 15 cubic feet of air remaining.
To answer this, we need to set up an inequality that represents this situation. The diver starts with 80 cubic feet of air, and after t minutes, at a rate of 1.2 cubic feet per minute, the diver has used 1.2t cubic feet of air. The remaining air in the tank will be 80 - 1.2t. The diver must surface when this remaining air is at least 15 cubic feet, so we get the inequality:
80 - 1.2t ≥ 15
To find the maximum amount of time t the diver can stay underwater, we solve the inequality for t:
80 - 15 ≥ 1.2t
65 ≥ 1.2t
≈ 54.17 minutes
Since the diver has to surface before reaching exactly 15 cubic feet, we should not round up. Therefore, t ≤ 54 minutes. This corresponds to answer choice a.