Let's use the variable d to represent the distance between the cities.
The expression "one-fourth the distance between two cities" is equivalent to "(1/4)d"
This expression is 100 miles less than two-thirds of the distance, that is, "(2/3)d - 100"
These two expressions are equal, so we can write the equation:
[tex]\frac{1}{4}d=\frac{2}{3}d-100[/tex]
Therefore the correct option is B (second one).
