MathNet 2025-part-01 — 187 problems (EN–VI) Question 143

Let triangle $ABC$ be equilateral with side length $a$ meters. Point $X$ moves from vertex $A$ toward $C$ at $3$ m/s, and point $Y$ moves from vertex $B$ toward $C$ at $4$ m/s, both starting at the same time. After how many seconds will the distance $XY$ be equal to the height of triangle $ABC$?
(Khulan Tumenbayar)