Tom travels for $10$ minutes longer than Tim, a time of $1$ hour and $50$ minutes.

Travelling at a speed of $60$ mph (or $1$ mile per minute), Tom travels a distance of $110$ miles.

Tim travelled the sam distance in $1$ hour $40$ minutes ($1\frac{2}{3}$ hours), so his speed, in mph was $110\div 1\frac{2}{3} = 110\times \frac{3}{5} = 22\times 3 = 66$ mph.

*This problem is taken from the UKMT Mathematical Challenges.*