smc

Let $p(t)=24t$ be the number of feet the powderman is from the blast at $t$ seconds after the fuse is lit, and let $q(t)=1080t-32400$ be the number of feet the sound has traveled. We want to solve for $p(t)=q(t)$. $$24t=1080t-32400$$ $$1056t=32400$$ $$t=\frac{32400}{1056}$$ $$t=\frac{675}{22}=30.6\overline{81}$$ The number of yards the powderman is from the blast at time $t$ is $\frac{24t}{3}=8t$, so the answer is $8(30.6\overline{81})$, which is about $245$ yards. $\boxed{\text{245 yd.}}$