During a spiritual gathering, the devotees chant HARE-RAM HARE-RAM....

The time taken for the sound to travel to the building and reflect back to the listener is given by $t = \dfrac{2d}{v}$

Substituting the given values:

$t = \dfrac{2 \times 80}{320} = 0.5 \text{ s}$

For the echo not to disturb the listener, the reflected sound of the first chant must coincide with the chanting of the second one. If the time interval between the chants is greater than $0.5 \text{ s}$, the echo will be heard separately, causing a disturbance.

Thus, the maximum time interval that can be maintained between consecutive chants is $0.5 \text{ s}$.