Set up the time equation

The time taken to travel from P to Q is $\frac{d}{v}$ and from Q to P is $\frac{d}{v+10}$. The sum of these times is 9 hours.

$\frac{200}{v} + \frac{200}{v+10} = 9$

Simplify the algebraic expression

Factor out 200 and find a common denominator to combine the fractions.

$200 \left( \frac{v+10+v}{v(v+10)} \right) = 9 \implies 200(2v+10) = 9(v^2 + 10v)$

Formulate and solve the quadratic equation

Expand the terms and rearrange into the standard form $av^2 + bv + c = 0$.

$9v^2 + 90v - 400v - 2000 = 0 \implies 9v^2 - 310v - 2000 = 0$

Find the value of v

Using the quadratic formula or testing the given options, we find that $v=40$ satisfies the equation as $9(1600) - 310(40) - 2000 = 14400 - 12400 - 2000 = 0$.

$v = 40$