tework Two cars start out together from the same place. They travel in opposite directions, with one of them traveling 5 miles per hour faster than the other. After three hours, they are 423 miles apart. How fast is ea car traveling?

Let's break down the problem! If we let the speed of the slower car be \( x \) miles per hour, then the faster car's speed would be \( x + 5 \) miles per hour. After three hours, the distance traveled by the slower car is \( 3x \) miles and by the faster car is \( 3(x + 5) \) miles. The equation representing their total distance apart would be: \[ 3x + 3(x + 5) = 423 \] Simplifying this gives: \[ 3x + 3x + 15 = 423 \] \[ 6x + 15 = 423 \] \[ 6x = 408 \] \[ x = 68 \] So the slower car is traveling at 68 miles per hour, and the faster car is traveling at 73 miles per hour (since 68 + 5 = 73). To summarize: the slower car's speed is 68 mph, and the faster car's speed is 73 mph!