Let the distance between Newcastle and South Shields be $x$ miles. Then the time for the whole journey is $(\frac{x}{30}+\frac{x}{40})\mathrm{hours}=\frac{7x}{120}\mathrm{hours}$. Thus the average speed is $(2x÷\frac{7x}{120})\mathrm{mph}=\frac{240}{7}\mathrm{mph}=34\frac{2}{7}\mathrm{mph}.$