Currently, the Toyota Corolla is the best selling car in the world. Suppose that during a test drive of two Corollas, one car travels 224 miles in the same time that the second car travels 175 miles. If the speed of the first car is 14 miles per hour faster than the speed of the second car, find the speed of both cars.

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.

To find the speed of both cars, we can set up a system of equations based on the given information.

Let's assume the speed of the second car is "x" miles per hour. Therefore, the speed of the first car is "x + 14" miles per hour.

We can calculate the time taken for each car using the formula: time = distance / speed.

For the first car: time = 224 / (x + 14)
For the second car: time = 175 / x

Since both cars took the same amount of time, we can set these two expressions equal to each other:

224 / (x + 14) = 175 / x

Now, we can solve this equation to find the value of x, which represents the speed of the second car.

To do that, we'll use cross-multiplication:

224 * x = 175 * (x + 14)

Simplifying further:

224x = 175x + 2450

Subtracting 175x from both sides:

224x - 175x = 2450

49x = 2450

Dividing both sides by 49:

x = 2450 / 49

Simplifying:

x = 50

Therefore, the speed of the second car is 50 miles per hour.

To find the speed of the first car, we can substitute the value of x back into the equation:

Speed of the first car = 50 + 14 = 64 miles per hour.

So, the speed of the first car is 64 miles per hour, and the speed of the second car is 50 miles per hour.