Final answer:
To find the speed of both cars, set up two equations using the distance traveled and the speed of the cars. Solve the equations to find the speeds of the cars.
Step-by-step explanation:
To solve this problem, let's first let x represent the speed of the second car. Since the speed of the first car is 14 miles per hour faster, the speed of the first car can be represented as x + 14.
We know that the distance traveled by both cars is equal to their respective speeds multiplied by the same time. So, we can set up the equation 252 = (x + 14) * t and 210 = x * t, where t represents the time taken for both cars.
From the second equation, we can express t in terms of x: t = 210 / x. Substituting this into the first equation, we get 252 = (x + 14) * (210 / x). Simplifying the equation, we have 252 = (210 + 14x) / x.
Cross-multiplying, we get 252x = 210 + 14x.
Combining like terms, we have 238x = 210. Dividing both sides by 238, we find that x ≈ 0.88. Therefore, the speed of the second car is approximately 0.88 miles per hour.
The speed of the first car can be found by adding 14 to the speed of the second car, so the speed of the first car is approximately 0.88 + 14 = 14.88 miles per hour.
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