Will prayer be answered quickly?

No, they rarely are.
One of the key factors in realising particularly miracles of healing is persistence in prayer. Much divine assistance is missed at healing services and renewal meetings because we lack understanding of this.
We think that when we have prayed once it is all up to God to give and the sufferer to receive. There seems to us to be nothing more we can do about it. We forget that Christ has entrusted his ministry of Kingdom miracles to us.
We are actually expected to keep going until we reach the desired objective.
This idea of persistence is not to be confused with being faithful. Faithfulness is vital too, of course, but persistence is the further ingredient which is so essential. It demonstrates trust.
It is often tempting to receive prayer and then give up when the desired healing does not quickly arrive, but this is illogical. We would not take that approach when visiting the doctor’s surgery.
If our local medical practitioner were to diagnose some skin disease, for example, and then write out a prescription note for us to take to the pharmacy, we would not then throw down the note before even crossing the street when we realise that the disease has not yet left us.
On the contrary, we acquire the medicine and continue with it until the required effect is achieved. If this does not happen in the expected time–frame then we are encouraged to re–visit the doctor for further treatment.
In the same way, divine blessings are something that, generally speaking, have to be pursued.
As we press up into God so he presses down to us. He responds to persistent expectancy as he draws us to his knee.
This is not to say that a demonstrable improvement in our condition cannot be gained within minutes. That can happen. It does mean that persistence is a vital element in our faith expectancy.
If we expect that divine healing should always be instantaneous then we will be led into doubt when that is not the way it happens, for we begin to think, quite wrongly, that healing might not be God’s will for the person.
It is always God’s will, and we need to press into it.