Tom drove from P to Q

Let the distance of P to Q be L.

Time needed for the first ride= $\frac{L}{30}$

Time needed for the second ride= $\frac{L}{X}$

Total time needed= $\frac{2L}{45}$

So, we solve the following equation, $\frac{L}{30}$ + $\frac{L}{X}$ = $\frac{2L}{45}$

We derive X=90

To calculate an average speed, one uses the harmonic mean , since the vehicle spends the same distance at each speed, not the same time .

$\begin{aligned} \frac{2}{\frac{1}{30}+\frac{1}{x}} &= 45 \\ \frac{1}{30}+\frac{1}{x} &= \frac{2}{45} \\ x+30 &= \frac{4}{3}x \\ x &= \boxed{90} \end{aligned}$

Let the distance between $P$ and $Q$ be $D$ . Then the time it took Tom to drive from $P$ to $Q$ is $t_1 = \dfrac D{30}$ hours and that from $Q$ to $P$ is $t_2 = \dfrac DX$ hours. The the average speed is given by:

$\begin{aligned} \frac {2D}{t_1+t_2} & = 45 \\ \frac {2D}{\frac D{30}+\frac DX} & = 45 \\ \frac {60X}{X+30} & = 45 \\ 4X & = 3X + 90 \\ \implies X & = \boxed{90} \end{aligned}$