Esther -
You're doing great!

Don't be discouraged - it's not taking you long. I'm 50 and have just started as well, having done really no exrecise prior to this. A few weeks ago I was struggling to do 4 miles but its amazing how quickly it builds up. I did 20 miles yesterday, pretty dead flat (nearly killed me!) but I'd never have thought I'd have made such big progress in a relatively short time. I'm going slower than you tho' - average 9mph. The important thing is to do what feels comfortable for you and enjoy it!
I was cycling along a canal towpath yesterday and when things were feeling grim I reminded myself to look at the scenery and relax - it's not a test!

There's some good advice on the thread 'Which gear?'. I was intially making it hard for my self by riding in too big a gear.

One of the most helpful peices of advice came from Geonz who said to get away from feeling like you are pedling up and down and think of it as peddling 'round and round'. This really helped me on my ride yesterday. It somehow makes it easier....not sure why.