Cryptography (Public-private key cryptography)--Logical thinking problem

Both A and B were on two islands. B is sick, and a has the medicine that B needs. C has a boat and a lockable box.
C is willing to carry things between A and B, but things can only be placed in boxes. As long as the box is unlocked, C will steal everything from the box,
No matter what's in the box. If A and B each have a lock and can only open the key of their own lock, how should a be delivered to B?

Answer: A put the medicine in the box, lock the box with your own locks. b After getting the box, add a lock on the box. After the box is shipped back to a, a takes off its own lock. When the box is transported to B, B takes off his lock and gets the medicine.

So, a put the medicine into the box, with its own public key to lock the box, then others do not know A's private key will not open. C After the box to B, b with its own public key to add a lock.
At this time the box has two locks. Give A,a to open his own lock with the private key. Give b again, it's ready.

Cryptography (Public-private key cryptography)--Logical thinking problem