Answer: 66 mph

Tom starts	60 miles per hour	1 hour 50 minutes = 110 minutes
Tim starts 10 minutes later	speed unknown	1 hour 40 minutes = 100 minutes

Finding the distance
Tom: 60 miles per hour $\Rightarrow$ 110 miles in 110 minutes

Tim travels 110 miles in 100 minutes
                  11 miles in 10 minutes
                  66 miles in 1 hour


Using ratio
Both travel the same distance.
Times in ratio 110 : 100
$\therefore$ speeds in ratio 100 : 110 = 10 : 11 = 60 : 66


Using algebra
Say Tim's speed is $v$.

Tom and Tim travel the same distance, so $$\begin{align}
60\times1\frac56 &= v\times 1\frac46\\
\Rightarrow 110&=\frac53v\\
\Rightarrow 22 &= \frac13v\\
\Rightarrow 66 & =v \end{align}$$