Can you help me to translate this sentence into English?
I will take Topik on Sunday, and now in 41듣기, 4 question, i must choose a good answer to fill in the blank. In one of 4 answer, i saw an answer as follows;:
도저히 시간이 안 될 것 같아요.
i know almost of the words in this answer, but i can't understand it's meaning. can you help me to understand it? Thank!

Question

Answer

It is polite way to say "I cannot allow my time at all". So in natural way, "It would be difficult for me to make time for it."

*시간이 되다: able to make time for it
 ex. Q."너 그날 시간 되?"=Are you available on that day? 
        A."아니, 난 시간이 안되"="어려워"=No

*When you use "~같아요", it makes the meaning less stronger, like when you are not certain or you're just assuming.

Hope it helps you !
HYEEUN혜은

Answer

It seems like it/he/she doesn't have time at all?