Let

*x* = distance between

*A* and

*B* in kilometer

*v* = original velocity (velocity during the 1st half of the distance

*AB*)

From *A* to *B*

$\dfrac{0.5x}{v} + \dfrac{0.5x}{v - 0.5} = 5.5$ ← Equation (1)

From *B* to *A*

$\dfrac{x}{v + 1} = 3.75$

$v = \dfrac{x}{3.75} - 1$

From Equation (1)

$\dfrac{0.5x}{\dfrac{x}{3.75} - 1} + \dfrac{0.5x}{\left( \dfrac{x}{3.75} - 1 \right) - 0.5} = 5.5$

$x = 15 ~ \text{km}$ *answer*