Final answer:
The speed of a car that takes 23 hours to travel between two cities, when it takes 10 hours at 69 mph, is calculated using inverse variation to be 30 mph.
Step-by-step explanation:
The correct answer is that the speed of a car that makes the trip in 23 hours is 30 mph.
Since the time taken to cover a distance between two cities varies inversely with the speed of the car, we can use the inverse variation formula, which is time_1 * speed_1 = time_2 * speed_2. We know from the given information that time_1 = 10 hours and speed_1 = 69 mph.
To find speed_2 for time_2 = 23 hours, we set up the equation as follows:
10 hours * 69 mph = 23 hours * speed_2
690 = 23 * speed_2
speed_2 = 690 / 23
speed_2 = 30 mph
Therefore, a car that takes 23 hours to make the same trip would be traveling at 30 mph.