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I'm having trouble understanding why 13.5 s is incorrect.

Here is my approach:

T_position = 19(m/s)t + 50.4m (50.4 = Car length + Truck Length + Distance in beteen)

C_position = .275(m/s^2)t^2 + 19(m/s)t

C_position corresponds to the rear of the car, and T_position the front of the truck.

Solving for both position equations yields:

50.4m = .275(m/s^2)t^2

sqrt(50.4/.275) = t = 13.5s