When God's provision comes from unexpected places!
1 Kings 17:9 Go at once to Zarephath of Sidon and stay there. I have commanded a widow in that place to supply you with food.
Again, it would have been incredibly hard for Elijah, for not only is it a place of Baal worship, but he is also going to a widow who God has commanded to provide for him... and she is also a Gentile widow. Jews did not, in those days, associate with Gentiles. But God is actually calling him there and is saying 'look, even though this doesn't appear to be normal, I am going to provide for you in this area'. This woman actually gets a mention in the New Testament. She would never have believed that her life would go down in history, but Jesus refers to this woman in Luke chapter 4.
Luke 4:16-30 He went to Nazareth, where he had been brought up, and on the Sabbath day he went into the synagogue, as was his custom. And he stood up to read. (17) The scroll of the prophet Isaiah was handed to him. Unrolling it, he found the place where it is written: (18) The Spirit of the Lord is on me, because he has anointed me to preach good news to the poor. He has sent me to proclaim freedom for the prisoners and recovery of sight for the blind, to release the oppressed, (19) to proclaim the year of the Lord's favor." (20) Then he rolled up the scroll, gave it back to the attendant and sat down. The eyes of everyone in the synagogue were fastened on him, (21) and he began by saying to them, "Today this scripture is fulfilled in your hearing." (22) All spoke well of him and were amazed at the gracious words that came from his lips. "Isn't this Joseph's son?" they asked. (23) Jesus said to them, "Surely you will quote this proverb to me: 'Physician, heal yourself! Do here in your hometown what we have heard that you did in Capernaum.' " (24) I tell you the truth, he continued, "no prophet is accepted in his hometown. (25) I assure you that there were many widows in Israel in Elijah's time, when the sky was shut for three and a half years and there was a severe famine throughout the land. (26) Yet Elijah was not sent to any of them, but to a widow in Zarephath in the region of Sidon. (27) And there were many in Israel with leprosy in the time of Elisha the prophet, yet not one of them was cleansed--only Naaman the Syrian." (28) All the people in the synagogue were furious when they heard this. (29) They got up, drove him out of the town, and took him to the brow of the hill on which the town was built, in order to throw him down the cliff. (30) But he walked right through the crowd and went on his way.
This is the first sermon of Jesus. He was comparing His present time in Israel to that of Elijah and Elisha. So if you have not been accepted for anything you have said about the Lord, you are in good company! What Jesus was doing was comparing His day to that of Elijah and Elisha's time. Those were dark days; the land was absolutely polluted and God's judgment was upon it. What Jesus is saying here to these people is 'you are going to reject Me, and you are going to reject My message in the same way that Elijah was rejected'. For this reason they wanted to kill Him and it says that they led Him out to the cliff and were going to try and throw Him over but it wasn't yet God's time for Him to die - especially in that way. God had another purpose for Him, so He passed through the crowd. But He mentions the widow here that Elijah was sent to. There were many widows in Israel, but it is only to this one that Elijah was sent. So she gets a mention in the New Testament of someone who actually had faith and someone that God used to provide and make provision for the prophet.
So back to 1st Kings... It would have been incredibly hard for Elijah to go to Zarephath. The whole land is searching for him as Jezebel wants to take his life because of what he had said. And Elijah goes and hides in her father's home town where she was brought up! It is a little bit like when they were looking for Osama Bin Laden and he was right under their nose. The other thing God is saying here is that sometimes a door will close, just like the brook drying up - that is a closed door. However another door will always open. When the brook dried God provided someone else to make provision. You don't expect God to act or work in this way, but Elijah was called to trust what God had planned.