Explaining the appropriate duration between the adhan and the iqamah

Question:
What is the appropriate duration between the adhan and the iqamah?

Answer:
There is no fixed limit between the adhan and the iqamah, but the imam should aim for the right time. I do not know of a fixed limit from the Prophet (peace and blessings be upon him) other than that he should aim for about a quarter of an hour, a third of an hour, or something close to that, depending on how close the ma'mum are and how quickly they rush to pray.
So if they rush to the prayer and gather quickly, he should hasten it. If there is some delay on their part, he should consider their circumstances, especially in the 'Isha' prayer. The Prophet (peace and blessings be upon him) sometimes considered their situation regarding the 'Isha' prayer; sometimes, if he saw they were hastening, he would hasten it, and if they were slow, he would delay it.
As for the Zuhr, 'Asr, Maghrib, and Fajr prayers, the imam should consider their situation in these and not delay too much. Rather, he should aim to pray at the beginning of the time, but without haste. However, for the Maghrib prayer, it is better to hasten it shortly after the adhan. The Prophet (peace and blessings be upon him) would hasten it shortly after the adhan, and the Companions would pray two rak'ahs after the adhan, then the Prophet (peace and blessings be upon him) would come and give the iqamah.