web.config conflicts in virtual directories

In IIS, I have two web applications configured as follows:

Website 1 (fixed IP)
Application A
page1.aspx
web.config

Application B
page1.aspx
web.config


each of the web.config files contain a connection strings block with
one connection string ("connection 1"). When I try to open
application B in my browser, I get the following error:

Entry Connection 1 has already been added

indicating that although I'm requesting Application B, both web.config
files are being read and a conflict has arisen. I can fix this by
running Application B in a separate application pool, but I'd like to
know what's causing it. I cannot seem to reproduce this problem in my
development environment.

Bill E.
.