Let v be the man's present speed, in kilometers per hour.

Then the other, hypothetical speed is (v+10) km/h.


The time to drive 100 km at the speed v      km/h  is    hours.

The time to drive 100 km at the speed (v+10) km/h  is    hours.


The problem says that time    is 30 minutes, or 1/2 of an hour less than time  .

So, we write this time equation

    -  =   of an hour.


At this point, the setup is complete.
To solve this equation, multiply its terms by 2v*(v+10) in both sides.
You will get

    100*2*(v+10) - 100*2*v = v*(v+10),

    200v + 2000 - 200v = v^2 + 10v

    v^2 + 10v - 2000 = 0.


Factor left side

    (v+50)*(v-40) = 0.


This equation has two roots,  v= -50  and v= 40.


Since v should be positive, due to its meaning, we accept the positive root v= 40 km/h
and deny the negative root.


So, the ANSWER  to the problem is that the present speed of driving is 40 km/h.


CHECK.  Driving time at the present speed is   = 2 hours.

        Driving time at the speed of 40+10 = 50 km/h  is   = 2 hours.

        The difference of the two driving times is 1/2 of an hour, or precisely 30 minute,

        which confirms that the answer is correct.