Final answer:
The average speed of the swimmer would be 4 feet per second if it takes 150 seconds to finish the race, based on inverse proportionality between race time and speed. The correct answer is option 1.
Step-by-step explanation:
The question asks us to find the average speed of the swimmer given that the time to swim a race is inversely proportional to the swimmer's average speed. We are informed that the swimmer finishes a race in 120 seconds with an average speed of 5 feet per second. To find the new speed when it takes 150 seconds to finish the race, we set up a proportion where the product of the speed and time is constant according to the principle of inverse variation.
We know that speed1 x time1 = speed2 x time2. Plugging in the values we have:
5 ft/sec x 120 sec = speed2 x 150 sec
To find speed2, we solve the following equation:
speed2 = (5 ft/sec x 120 sec) / 150 sec
speed2 = 600 ft / 150 sec
speed2 = 4 ft/sec
Therefore, if it takes 150 seconds to finish the race, the average speed of the swimmer would be 4 feet per second.
The correct option is 4 ft/sec.