Dick had no appetite for the food but he managed to chew his way silently through it.
I don't understand the construction after 'he managed to'.

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It means he ate ("chewed") the food without making any complaints, even though he didn't like it.  In other words, he was polite.

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Alexander, 

In this sentence "to manage to" means " to succeed in accomplishing ". 

Dick had no appetite for the food but he succeeded in chewing his way silently through it. 


ему удалось = he managed to

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dick should try making a milkshake :P