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

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 = x

Westbound 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 hours

Distance between trains after 3 hours = 468 miles

2. Let's find the speed of each train, using the following equation:

3x + 3 (x + 3) = 468

3x + 3x + 9 = 468

6x + 9 = 468

6x = 468 - 9 (Subtracting 9 at both sides)

6x = 459

x = 459/6 (Dividing by 6 at both sides)

x = 76.5 miles per hour

The 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 correct

3x + 3 (x + 3) = 468

3 (76.5) + 3 (76.5 + 3) = 468

229.5 + 238.5 = 468

468 = 468

The 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.