Explanation:
To make \( q \) the subject of the formula in the equation \(\frac{q-r}{t} = \frac{v-q}{v}\), we will follow these steps:

Step-by-Step Solution:

1. Cross multiply to eliminate the fractions:

\[
v(q - r) = t(v - q)
\]

2. **Expand both sides:**

\[
vq - vr = tv - tq
\]

3. Collect all terms involving \( q \) on one side of the equation:

\[
vq + tq = tv + vr
\]

Combine like terms:

\[
q(v + t) = vr + tv
\]

4. Solve for \( q \):

\[
q = \frac{vr + tv}{v + t}
\]

Factor out the common terms in the numerator:

\[
q = \frac{v(t + r)}{v + t}
\]

The correct answer is A - \( q = \frac{v(t+r)}{v+t} \)