The hike started at 9am at a walking speed of 6km/h. After 1½ hrs (at 10.30am) the hikers have walked 9km. We can use the equation d=9+6t where d is distance walked after a time t hrs after 10.30am.
Driving at 60km/h distance travelled d=60t. These two distances are the same when they meet at time t, where 9+6t=60t, 54t=9, t=9/54=⅙hr=60/6=10 minutes. So she catches up at 10.30+10mins=10.40am (d=10km).