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To solve the problem, we need to set up an equation based on the information given.
Let's denote the length of the mountain trail as "x" miles. Since two-thirds of the total distance of 10 miles is over the mountain trail, we can say that (2/3) * 10 = x.
Now, the equation becomes:
(2/3) * 10 = x
We can simplify this equation as:
20/3 = x
So, the mountain trail is 20/3 miles long.
Now that you have the equation, you can solve it by simplifying and calculating the value of x. In this case, the mountain trail is 20/3 miles long.