Answer:
Yes, the race car driver needs a faster reaction time than someone driving in a school zone.
Explanation.
For the sake of argument, let us consider
(i) a person driving at 35 mph in a school zone (as a normal driver);
(ii) a person driving at 60 mph in a school zone (as a racing driver).
Suppose a blind pedestrian crosses the road 0.1 miles (about 500 feet) in front of the driver.
The time before the normal driver hits the pedestrian is
(0.1 /35)*3600 = 10.3 seconds.
The time before the racing driver hits the pedestrian is
(0.1/60)*3600 = 6 seconds.
Because a reaction time of 6 seconds may be insufficient to avoid hitting the pedestrian, the racing driver needs a faster reaction time than the normal driver.