, 2025

Let $x$ be the number of
minutes that it would take the bigger ant to build an anthill alone and
let $y$ be the number of minutes that
it would take the smaller ant to build an anthill alone.

Since the bigger ant can build an anthill in $x$ minutes, the bigger ant builds $\dfrac{1}{x}$ anthills per minute.

Likewise, the smaller ant can build $\dfrac{1}{y}$ anthills per minute.

Thus, working together, the two ants build $\dfrac{1}{x}+\dfrac{1}{y}$ anthills per
minute.

It is also given that it takes the two ants $24$ minutes to build an anthill together,
so this means they build $\dfrac{1}{24}$ anthills per minute working
together.

Hence, we get the equation $\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{24}$.

Multiplying this equation through by $24xy$ gives $24y+24x=xy$.

From the other given condition, we get $x=y-14$, so we can substitute to get $24y+24(y-14) = (y-14)y$.

Expanding and rearranging, this equation becomes $y^2-62y+336=0$, which can be factored as
$(y-56)(y-6)=0$.

If $y=6$, then $x=-8$, which does not make sense since
$x$ must be positive. Therefore,
$y=56$.