Hit the 3,000 km mark

My daily commute is 36 km (22.5 miles) and features a fairly brisk ride into Vancouver from our 200m mountain elevation down to sea level, during which I average about 23 km/hr over the 40 minute ride and considerably less on the return. On the ride home the 200m elevation is recovered via a very steep climb for about 1.2kms (that reclaims about 150m of elevation) followed by a gradual 2.5km that recovers the rest.

It doesn't compare at all to the 100km climbs in The Tour de France, and while I think most people my age would find it hard to do, a reasonably fit person could certainly match my time. I was regularly getting into work in about 40 minutes and back home in about 55, but I replaced the chain and rear cogset and this really slowed me down.  The "cogset" is the mass of teeth on the back wheel, and is the partner to the "chainring" at the center of the bike, which is powered by the cyclist's feet. When a cyclist changes gears, one gear shifter moves the chain up and down each "sprocket" in the cogset, and another moves the chain around the chainring. Competitive bikers adjust the cogset to suit the course, and for long, straight journeys they would go with a cogset with fewer teeth to generate speed, and for steep courses they would opt for many teeth to help them climb. For a course with varied terrain they need both, and for single track courses in a velodrome they probably just need a single speed.

The rear cogset is connected to the chainring by the chain and creates the "drivetrain."  I was given my bike for free, and after learning more about bike repair I saw that the chain was old and stretched out, and had whittled away the teeth on the cogset.  It's simple to understand because the chain and teeth work in unison, and and if the chain doesn't align with the teeth anymore then it grinds away at the teeth where there's friction. 

I bought a new chain and cogset (called a cassette if all the sprockets are together) but was erroneously given a 7-sprocket one to replace my 8-sprocket cogset. I installed it, and then attached the smallest sprocket from the old cogset so the chain wouldn't fall off.  That small sprocket has the fewest teeth, and is the one a cyclist uses to go really fast, but I had to disable it because it had been ground down by the old chain and didn't mesh with the new chain. So I can't use this sprocket to achieve high speeds and I wind up coasting a lot.

I'll have to replace the cogset , but ideally would like to wait for a few thousand kms so as to not waste the money I spent.  I'll wait and see if my time is being constrained a lot because of this.