Let's assume the speed of the second car (slower car) is x miles per hour.
Given that the first car (faster car) travels 14 miles per hour faster than the second car, the speed of the first car can be expressed as (x + 14) miles per hour.
Now, let's calculate the time taken for each car to cover their respective distances using the formula:
Time = Distance / Speed
For the first car: Time taken = 224 miles / (x + 14) miles per hour
For the second car: Time taken = 175 miles / x miles per hour
Since both cars traveled the same amount of time, we can set up an equation:
224 / (x + 14) = 175 / x
To simplify the equation, we can cross-multiply:
224x = 175(x + 14)
Expanding the equation:
224x = 175x + 2450
Bringing all the terms to one side:
224x - 175x = 2450
Combining like terms:
49x = 2450
Dividing both sides of the equation by 49:
x = 50
Therefore, the speed of the second car (slower car) is 50 miles per hour.
To find the speed of the first car (faster car), we can substitute the value of x into the expression:
Speed of the first car = x + 14 = 50 + 14 = 64 miles per hour
Hence, the speed of the first car is 64 miles per hour, and the speed of the second car is 50 miles per hour.