It's not possible to answer the question exactly the way it's written.
That's because we don't know anything about the direction they
drive at any time during the trip.
You see, "velocity" is not just a word that you use for 'speed' when
you want to sound smart and technical, like this question is doing.
"Velocity" is a quantity that's made up of speed AND THE DIRECTION
of the motion. If you don't know the direction of the motion, then you
CAN'T tell the velocity, only the speed.
Here are the average speeds that Lori's family drove on each leg
of their trip:
Speed = (distance covered) / (time to cover the distance) .
Leg-A:
Speed = 15km/10min = 1.5 km/min
Leg-B:
Speed = 20km/15min = (1 and 1/3) km/min
Leg-C
Speed = 24km/12min = 2 km/min
Leg-D:
Speed = 36km/9min = 4 km/min
Leg-E:
Speed = 14km/14min = 1 km/min
From lowest speed to highest speed, they line up like this:
[Leg-E] ==> [Leg-B] ==> [Leg-A] ==> [Leg-C] ==> [Leg-D]
1.0 . . . . . . . . 1.3 . . . . . . . 1.5 . . . . . . . 2.0 . . . . . . . 4.0 . . . . km/minute
Whoever drove Leg-D should have been roundly chastised
and then abandoned by the rest of the family. 36 km in 9 minutes
(4 km per minute) is just about 149 miles per hour !