For what size of a strip?
1/4 x 3/4 strips which are well fit and closely clamped can be good in 15 minutes. Not full strength but enough to allow a second strip to be fit and glued.
That assumes you can put the strip in place without excessive force. If you have lots of twist, you might need to use a heat gun to bend the strip so it fits without much force. If you can't it may take a lots longer.
A sloppy fit (including touching on the outside and a gap inside) can take a day. Sometimes it will not ever really harden up if you have a .030" or bigger gap.