To make you think clearly,

Assume the speed of your car is infinite,

Then Your car driver will only leave your home almost "ZERO" seconds
before your air plane's original arrival time in order to meet you on
time,

in these case if you walk to home and arrive at home 20 mins before
schedule, the only possibility is "the distance from airport to your home
is 40 mins walking time and you walked 40 mins to get home and your
driver will leave 20 mins later as planed" , as you see in these case you
will not meet your driver in the middle of road.

Now make a more sensible estimation of the speed of your car, Say
Your car's speed is 6 times of your walking spped, in order to make
conditions consistent, the walking time from air port to home is 60
mins walking time and 10 mins driving time, in this case you walked
60 mins to get home and your driver is just about to hit on the road.
So you meet your driver in your garage.

What about your car's speed is 5 times of your walking speed,
the distance is 100 mins walking time and 20 mins driving time.
you will meet your driver/car at exactly the "1/2" mark of the road.

What about your walking speed is the same as car speed, the distance is
60 mins and you will walk 10 mins to meet your car and 20 mins ahead
of you schedule.

So you see where to meet your car depends on the relative speed of
your car and walking. In order to meet your car in the middle of road
your car's speed must be less than 6 times of your walking speed otherwise you will walk all the way to home and if your car's speed is
m ( 0<m<6) times of your walking speed, you will have to walk 10m
mins to meet you car and 20 mins ahead of your schedule. Now you see
there is a great benefit of owning a "slow" car.