It is noteworthy that even though God has knowledge and understanding of all, and even sees the very thoughts of the soul, as Moses asserts (Dt. 31:21), it is said when he provides a remedy for us in our needs that he sees them, and when he answers our prayers that he hears them.
Not all needs and petitions reach the point at which God, in hearing, grants them. They must wait until in his eyes they arrive at the suitable time, season, and number, and then it is said that he sees and hears them.
This is evident in Exodus. After the 400 years in which the children of Israel had been afflicted by their slavery in Egypt, God declared to Moses: I have seen the affliction of my people and have come down to free them [Ex. 3:7-8], even though he had always seen it.
And St. Gabriel, too, told Zechariah not to fear, because God had heard his prayer and given him the son for whom he had prayed those many years, even though God had always heard that prayer [Lk. 1:13].
Every soul should know that even though God does not answer its prayer immediately, he will not on that account fail to answer it at the opportune time if it does not become discouraged and give up its prayer. He is, as David remarks, a helper in opportune times and tribulations [Ps. 9:9].
Saint John of the Cross
The Spiritual Canticle, Stanza 2, no. 4
At The Peacock's Perch 
Lance,
It occurs to me that the person or people doing the praying need to be clear about what they want. God may answer, but the result may not be to that soul’s liking or even of benefit, at least in the short term.
I can wish for specific outcomes, but when it comes to supplication, I always have to fall back on “Thy Will be done.”
Exactly, Katherine. Thy will be done. We often pray as if God’s need to learn from us what we need! How arrogant.
It seems the act of praying helps us to clarify what we want. As we ponder, we (I) often find I don’t really know the specifics, so Thy Will be done helps insure the best outcome(s) for all involved.