Answer :
Final answer:
One train is traveling at a rate of 91 mph and the other train is traveling at a rate of 78 mph.
Explanation:
Let's denote the rate of one of the trains as x mph. Since the other train is traveling 13 mph slower, its rate can be represented as x - 13 mph.
When the two trains travel towards each other, the total rate at which they cover the distance is the sum of their individual rates. Therefore, we have the equation:
x + (x - 13) = 676 / 4
Simplifying the equation, we get:
2x - 13 = 169
Adding 13 to both sides, we get:
2x = 182
Dividing both sides by 2, we find:
x = 91
Therefore, one train is traveling at a rate of 91 mph and the other train is traveling at a rate of (91 - 13) = 78 mph.