Answer
See the detailed answer below.
Work Step by Step
We will hear a minimum sound intensity when the path length difference between the two sound waves is given by
$$\Delta r=\left[m+\frac{1}{2}\right]\lambda$$
where $\lambda=v/f$;
$$\Delta r=\left[m+\frac{1}{2}\right]\dfrac{v}{f}\tag 1$$
From the geometry of the given graph,
$$\Delta r=r_2-r_1$$
where $r_1=x$, and $r_2=\sqrt{3^2+x^2}$,
So
$$\Delta r=\sqrt{3^2+x^2}-x$$
Plugging into (1);
$$\sqrt{3^2+x^2}-x=\left[m+\frac{1}{2}\right]\dfrac{v}{f} $$
Plugging the known;
$$\sqrt{3^2+x^2}-x=\left[m+\frac{1}{2}\right]\dfrac{343}{686} $$
$$\sqrt{3^2+x^2}-x=\frac{1}{2}\left[m+\frac{1}{2}\right]=\frac{1}{2} m+1 $$
Thus,
$$\sqrt{3^2+x^2}-x= \frac{1}{2} m+\frac{1}{4} $$
Using any software calculator;
At $m=0$,
$$x=\color{red}{\bf 17.88}\;\rm m$$
At $m=1$,
$$x=\color{red}{\bf 5.63}\;\rm m$$
At $m=2$,
$$x=\color{red}{\bf 2.98}\;\rm m$$
At $m=3$,
$$x= {\bf 1.7}\;\rm m$$
but this is dismissed since you are moving away from 2.5 m, so you will not be at this point.
