BlockChain scalability: How does BlockChain process multiple parallel transactions? I just did some introductory research into blockchain technology and this is a breakdown of my understanding of how it works:

Scenario: Assume Trump wants to send Obama 5 bitcoins. As soon as this transaction is initiated:


miners in the peer to peer network will (individually?) start solving for the next valid hash in the block chain. ( does the peer network use the combined processing power to solve together, or do nodes solve individually independent of each other?)
Once the valid hash is discovered, the node that did the discovery will be rewarded with a set of bitcoins
The ledgers at each node will be updated with the Alice -> Bob transaction, while this newly discovered hash will be a representation of the same. This should approximately take  about 10 minutes?


Now there is a good chance my understanding is completely off, but my question is this:

Lets say 1000 transactions are initiated at the same time. Regardless of this, the peer network will be solving for the next hash in the blockchain which will verify 1 transaction. So the 1000 transactions will be verified sequentially as the miners proceed from one valid hash to the next.

If solving for one transaction takes approximately 10 minutes, this would mean to completely verify the 1000 transactions (initiated at the same time) it would take around 1000 x 10 minutes!

Clearly this problem is handled in someway in the real world as i'm pretty sure thousands of bitcoin transactions take place at any given time without a delay like this. Some clarification would be hugely appreciated. thanks!
You should probably read up a bit more, but here's some help:


  miners in the peer to peer network will (individually?) start solving for the next valid hash in the block chain. ( does the peer network use the combined processing power to solve together, or do nodes solve individually independent of each other?)


Nowadays miners work together in mining pools.  These are not part of the actual protocol, but is just the way the mining ecosystem has evolved.  As far as the Bitcoin protocol is concerned, you can look at an entire mining pool as an individual miner.  Each pool is responsible for trying to make their nodes work in parallel.


  Regardless of this, the peer network will be solving for the next hash in the blockchain which will verify 1 transaction


This is where you are wrong.  The hash is for a block of transactions, not an individual transaction.  For many reasons, it is advantageous to do the proof of work on blocks rather than transactions.  See this question for more explanation on that.

I hope this helps.