def is_available(time, duration, availabilities):
    """
    Helper function to check if the given time and duration fits within a known set of availability windows.
    Duration is assumed to be one of 30, 60 (meaning minutes).  Availabilities is expected to contain entries of the format HH:MM.
    """
    if duration == 30:
        return time in availabilities
    elif duration == 60:
        second_half_hour_time = increment_time_by_thirty_mins(time)
        return time in availabilities and second_half_hour_time in availabilities

    # Invalid duration ; throw error.  We should not have reached this branch due to earlier validation.
    raise Exception('Was not able to understand duration {}'.format(duration))