Final answer:
An increase of 0.1 seconds in reaction time causes the thinking distance to increase at both 30 mph and 70 mph. It increases by 1.34 meters at 30 mph and by 3.13 meters at 70 mph.
Step-by-step explanation:
To calculate how an increase of 0.1 seconds in reaction time affects the thinking distance at 30 mph and 70 mph, we can use the formula thinking distance = speed × reaction time. At 30 mph (which is approximately 13.4 m/s), the initial thinking distance with a reaction time of 0.5 seconds is 13.4 m/s × 0.5 s = 6.7 meters. If the reaction time increases to 0.6 seconds, the new thinking distance becomes 13.4 m/s × 0.6 s = 8.04 meters. Therefore, the thinking distance at 30 mph increases by 1.34 meters. At 70 mph (which is approximately 31.3 m/s), the initial thinking distance with a reaction time of 0.5 seconds is 31.3 m/s × 0.5 s = 15.65 meters. If the reaction time increases to 0.6 seconds, the new thinking distance becomes 31.3 m/s × 0.6 s = 18.78 meters. Therefore, the thinking distance at 70 mph increases by 3.13 meters. In conclusion, an increase in reaction time of 0.1 seconds causes the thinking distance to increase at both speeds. The correct answer is option (a): The thinking distance increases at both speeds.