smc

We assume that the clicks are heard at the head of the train. Then if the train's speed in miles per hour is $x$, we can convert it to clicks per minute: $$\frac{x\text{ mile}}{\text{hr}}\cdot \left(\frac{1\text{ hr}}{60\text{ min}}\right)\cdot \left(\frac{5280\text{ ft}}{1\text{ mile}}\right)\cdot \left(\frac{1\text{ click}}{30\text{ ft}}\right)=\frac{5280x}{1800}\cdot \frac{\text{click}}{\text{min}}.$$ Therefore every minute, on average, $5280x/1800$ clicks are heard. The number of clicks heard in $y$ minutes is $y\cdot 5280x/1800$, so the number of clicks heard in $1800/5280$ minutes is equal to $x$. In other words, the speed of the train in miles per hour is equal to the number of clicks heard in $1800/5280$ minutes, which is approximately one-third of a minute, or $\boxed{20\text{ seconds}}$.