Final answer:
By setting up and solving an algebraic equation using the information that the sum of the distances covered in 4 hours by both cars is 420 miles, the speeds of the cars are determined to be 60 mph and 45 mph for the first and second cars respectively.
Step-by-step explanation:
To find the speed of each car, we can set up an algebraic equation based on the given information. The distance between Kansas City and Denver is 420 miles. If we let the speed of the second car be x miles per hour, then the speed of the first car would be 3x - 75 miles per hour.
Since they meet after 4 hours, the total distance covered by both cars would be 4 times the speed of the first car plus 4 times the speed of the second car, which equals the total distance of 420 miles. Therefore, our equation is:
4(3x - 75) + 4x = 420
By solving this equation, we find the speed of both cars:
12x - 300 + 4x = 420
16x = 720
x = 45
So, the speed of the second car is 45 mph and the speed of the first car is 3(45) - 75 which is 135 - 75, giving us 60 mph. Therefore, the correct answer is:
- Speed of the first car: 60 mph
- Speed of the second car: 45 mph
Note that none of the provided options (A, B, C, D) match our calculated speeds, so there must be a mistake in the question or the options given.