Lower back pain stopping me.......

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(I am posting this thread in the New Riders forum as well, if that´s not OK please remove one of them!)
I am new to this terrific forum - a 54 year old/young Swedish woman who just discovered the joy of cycling and just bought my first racer, a Cannondale Synapse!
But there is a problem which holds me back. After about half an hour of cycling, my lower back starts to hurt. It gets worse and worse until I almost want to get off my bike and call my Man to come and pick me up.
I do rides of between 30 kilometers and 50 kilometers, trying to make an avarage of 25/kilometers an hour (not quite there yet but almost). But I am held back by my aching lower back. I start to wriggle and twist, I stand up and I do all sorts of things to stop the pain. To no avail.....
My bike is the right size and everything but it still hurts. I THINK it is a matter of being unfit and having little muscle in my back and tummy, but how do I get past that?
Should I bite the bullet and try to push through it, hoping that eventually I will have built up enough muscle to pass by this pain? Or are there exercises I could follow?
I am about to sign up to a 300 km ride next June, the famous Swedish "Vätternrundan" which I hope to finish under 14 hours. But as is it right now, I would be calling for a pickup in under 2 hours, because of my back pain....... I WILL, however, sign up for the race, and i WILL do it - but how??????? What can I do to fix my back??

I had something similar. Adjusting the height and moving the saddle forward helped immensely. I also did some back exercises as well as core training.