Final answer:
The correct equation for driving time when driving a mph above the speed limit is T(a) = 83 / (70 + a) + 38 / (75 + a), where 'a' is the additional speed above the speed limit.
Step-by-step explanation:
The question asks for the equation of driving time, T(a), when a trucker drives a mph above the speed limit. Considering a as the additional speed above the speed limit, the correct formula would take into account the increased speed at which the trucker is traveling. Thus, the time taken would be the distance divided by the newly increased speed.
Given two separate distances (one of 83 miles and another of 38 miles) and the corresponding speed limits (70 mph and 75 mph), we adjust the formula to incorporate the extra a mph speed. Hence the time, T(a), to cover both distances at the increased speeds would be:
T(a) = ∆(83 miles / (70 mph + a mph)) + ∆(38 miles / (75 mph + a mph))
Therefore, the correct equation would be Option A: T(a) = 83 / (70 + a) + 38 / (75 + a), which describes the total time to cover both distances at the respective increased speeds.