Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3mph greater than the speed of the eastbound train. After 3 hours, they are 468 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions

Answer:The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.Step-by-step explanation:1. Let's review all the information provided for solving this question:Eastbound train speed = xWestbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)Duration of trip = 3 hoursDistance between trains after 3 hours = 468 miles2. Let's find the speed of each train, using the following equation:3x + 3(x + 3) = 4683x + 3x + 9 = 4686x + 9 = 4686x = 468 - 9 (Subtracting 9 at both sides)6x = 459x = 459/6 (Dividing by 6 at both sides)x = 76.5 miles per hourThe Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.3. Proof that x = 76.5 is correct3x + 3(x + 3) = 4683 (76.5) + 3 (76.5 + 3) = 468229.5 + 238.5 = 468468 = 468The value of x = 76. 5 is correct. And now we know that the  Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.