Answer
$35$ min.
Work Step by Step
Distance traveled by either runner = (average speed)(time of travel).
If the speed is given in mph, the time is expressed in hours.
10 minutes =$\displaystyle \frac{10}{60}=\frac{1}{6}$ hours.
At a certain distance from the start, Mary and Janet will meet.
Janet will have been running for $t$ hours, covering $5t$ miles.
Mary will have been running $(t-\displaystyle \frac{1}{6})$ hours, covering $7(t-\displaystyle \frac{1}{6})$ miles.
The distances covered are equal:
$5t= 7(t-\displaystyle \frac{1}{6})$
$5t=7t-\displaystyle \frac{7}{6}$
$-2t=-\displaystyle \frac{7}{6}$
$t=\displaystyle \frac{7}{12}$ hours
In minutes, $\displaystyle \frac{7}{12}(60)=35$ min.
