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 = 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.
