Final answer:
Nicole will have to swim for at least 50 minutes to swim at least 2000 meters.
Step-by-step explanation:
To represent the situation, we can let 'x' represent the time Nicole needs to swim in minutes. Since she swims at a rate of 40 meters per minute, she will swim a distance of 40x meters in 'x' minutes. To find out how long she will have to swim to reach at least 2000 meters, we can set up the following inequality:
40x ≥ 2000
To solve the inequality, we divide both sides by 40:
x ≥ 50
Therefore, Nicole will have to swim for at least 50 minutes to swim at least 2000 meters.