To solve the equation $q = -\frac{1}{s}rt$ for $r$ in terms of $q$, $s$, and $t$, follow these steps:

1. Start with the original equation: $q = -\frac{1}{s}rt$

2. Multiply both sides of the equation by $-s$ to eliminate the fraction: $-sq = rt$

3. Finally, divide both sides by $t$ to solve for $r$: $r = \frac{-sq}{t}$

So, the solution for $r$ in terms of $q$, $s$, and $t$ is: $r = \frac{-sq}{t}$

Would you like more details or have any questions? Here are some related questions to consider:

1. What happens to $r$ if $t$ approaches zero?
2. How does the sign of $q$ affect the sign of $r$?
3. What would $r$ be if $q$, $s$, and $t$ are all positive?
4. How can this equation be used in a practical application?
5. Can $r$ be zero? If so, under what conditions?

Tip: When isolating a variable, be mindful of how multiplication or division by negative numbers affects the equation, particularly the signs of the resulting terms.