SOLUTION: I am trying to help my son with his homework, and it might as well be in a foreign language. If someone could help me understand how to solve this maybe I can figure out the rest.

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Question 647166: I am trying to help my son with his homework, and it might as well be in a foreign language. If someone could help me understand how to solve this maybe I can figure out the rest.
Two trains start at the same place traveling in opposite directions for 6 hours. After 3 hours they are 414 miles apart. How fast is each traveling if the rate of one train is 8 miles per hour faster than the other?
Thank you in advance.
Answer by colliefan(242) (Show Source):
You can put this solution on YOUR website!
Two trains start at the same place traveling in opposite directions for 6 hours. After 3 hours they are 414 miles apart. How fast is each traveling if the rate of one train is 8 miles per hour faster than the other?
Rate (or speed) of one train is x mph
Rate of the other is x+8 mph
The distance traveled is the speed times the number of hours so:
distance traveled by first train is 3 hrs * x mph or 3x
distance traveled by second train is 3 hrs * (x+8 mph) or 3(x+8)
The problem tells you that the sum of these two is 414 so:
3x + 3(x+8) = 414
3x + 3x + 24 = 414
6x + 24 = 414
6x + 24 - 24 = 414 - 24
6x + 0 = 390
6x = 390
x = 65

If the first train is traveling 65 mph and the second is going 8 mph faster or 73, in 3 hrs they would be 414 miles apart and so the solution is correct.