I think the answer to a is dT/dt = -k(T-Ts). For b is k=0.16/(50-Ts) ? Should Ts not be given so that k can be found without any unknowns? Don't give me the answers to c or d since I will proably manage them after getting b.
You are correct on both counts. That is the correct differential equation for (a), and it looks like they want a numerical answer to (b) but to get that, you would need to know what Ts is.
For part (d), it looks like they want you to use the numerical value from (b).
I didn't see skeeter's post earlier. You can get a solution by using the Ts from part (d), but you don't know if that's what the author intended. There's a problem with the question either way.