1. **State the problem:** We have two rectangles, A and B. Rectangle A has length 15 and width $w$. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. We need to find the width of rectangle B in terms of $w$. 2. **Write the ratio for rectangle A:** The length-to-width ratio is $$\frac{15}{w}$$. 3. **Set the ratio for rectangle B equal to that of rectangle A:** Let the width of rectangle B be $x$. Then, $$\frac{20}{x} = \frac{15}{w}$$ 4. **Solve for $x$:** Cross-multiply: $$20w = 15x$$ Divide both sides by 15: $$x = \frac{20w}{15} = \frac{4}{3}w$$ 5. **Interpretation:** The width of rectangle B is $\frac{4}{3}w$. **Final answer:** $\boxed{\frac{4}{3}w}$ which corresponds to option A.