"But He did not answer her with even a word. And His disciples came up and urged Him, saying, 'Send her away, because she keeps shouting behind us.'" (Matthew 15:23, NASB)
I believe the reason Jesus responded to the woman this way was to bring out, encourage and commend what is true faith.
You may recall that after Jesus seemed to be treating her rudely, and she kept pressing Him "in prayer," He finally said to her, "O woman, your faith is great; it shall be done for you as you desire." Maybe sometimes the reason for "delayed answers" is that Jesus wants fellowship with us, and not a "hit and run" relationship.
Father, in Jesus' Name, thank You for always wanting fellowship with me. Amen.
When Peter, an 18 year old Norwegian, "heard the call to evangelize China, on that day he not only emptied his wallet into the collection plate, but included a small note with the words, 'and my life.'"
Hebrews 12:2