Maria starts out jogging from Ye Olde Bridge at 8:00 a.m. at a speed of 4 mi/h.
Twelve minutes later, Nicole starts out from Ye Olde Bridge and follows the
same route. At what constant rate in miles per hour must Nicole run to catch
Maria at 8:42 a.m.? Express your answer as a decimal to the nearest tenth.
First, we find that Maria runs for $42$ minutes or $\frac{42}{60}=\frac{7}{10}$ of an hour. Since $d=rt$, we get that Maria visits $\frac{7}{10}\cdot 4=\frac{28}{10}=2.8$ miles. Thus, Nicole must run $2.8$ miles in $42$ minutes. $42$ minutes is $42/60=7/10$ hours, so $r=\frac{2.8}{7/10}=4\cdot\frac{2.8}{7}=4\cdot \frac{28}{70}=\boxed{1.6}$ miles per hour.
