r and q are inversely proportional variables. If q = 3/4 when r = 1/3, what is the value of q when r = 5?

Given that r and q are inversely proportional, we have:

q \propto \frac{1}{r}

or

q = \frac{k}{r}

where \( k \) is a constant.

Given:

q = \frac{3}{4} \; \text{and} \; r = \frac{1}{3}

We need to find the constant \( k \):

\frac{3}{4} = \frac{k}{\frac{1}{3}}

Thus,

\frac{3}{4} = 3k

Solving for \( k \):

k = \frac{1}{4}

Now, using \( r = 5 \):

q = \frac{k}{r} = \frac{\frac{1}{4}}{5}

q = \frac{1}{20}

Therefore, the value of \( q \) when \( r = 5 \):

q = \frac{1}{20}