If you put t= 4.16 into 450- 16t= 200+ 20t you get 450- 16(4.16)= 383.44 while 200+ 20(4.16)= 283.2. No, 4.16 is NOT the correct answer.
I am inclined to suspect that you subtracted wrong. Subtracting 200 from 450 gives 250 but if you accidently got 150 rather than 250, 150/36= 4.17.