Before the new road:
Section AP takes 20 minutes.
Section PB takes T/10 minutes, where T is the number of cars on the road.
Section AQ takes T/10 minutes.
Section QB takes 20 minutes.
So, the total time of travel from A to B before the new road is:
Total Time = 20 minutes (AP) + T/10 minutes (PB) + T/10 minutes (AQ) + 20 minutes (QB)
Now, with the new road that doesn't take any time, the total time of travel from A to B becomes:
Total Time = 20 minutes (AP) + 0 minutes (PQ) + 20 minutes (QB)
As you can see, the section PB and AQ times are no longer dependent on the number of cars (T/10), and they are replaced by the instantaneous PQ connection, which takes no time.
