Next time, see how long it will stay in one place using steering correction only (no actual strokes). You will soon start drifting with the current. Kayakers almost never steer this way, so you may be fooling yourself by steering with forward stroke to keep your bow into the current.

If this isn't the case, you've discovered a way to move through the water without any energy input, and your kayak should also travel forward on lakes without any need to paddle. Get it?

tough question to ask understandably I can see where my phrasing of the question has caused some confusion. Let me try it this way:

If I paddled on flat water at 3 miles per hour, then I can say that my canoe speed is accurately stated at 3 miles per hour.

But, if I paddle with the same boat and paddle with the same cadence and strength on moving water heading downstream, will my canoe speed up exactly the same as the flow of the river, or will there be a variation? So if my paddling speed is 3 and the river speed is 1 would I then be traveling at 4 mph?

Conversely, if my paddling speed is 3 mph and I’m now paddling upstream against a 1 mph current will my travel speed drop to 2 mph?

Mary is traveling at X mph
Jack is traveling at X mph

nothing including the planes flying overhead or the price of cheese in China make any difference.

If you are driving down a road at 40 mph does the wind speed effect the speedodometer. No
Does it effect your gas mileage? Yes
Does it effect how easy or hard you engine works? Yes

How long does it take to drive 20 miles at 10mph if gas cost $3.00/gal?

This is an entirely different question however your first question was and is the same as many trick questions. Also the same as questions that add more details and facts which confuse the reader who miss the original question.
A very good example of this can be found in the PFD post.
Read my first two (georgia_kayaker) postings then read the two responses following my second response. The do not relate to my previous 2 postings but they relate to my past history comments.
This comes from "not reading" the question.

"But, if I paddle with the same boat and paddle with the same cadence and strength on moving water heading downstream, will my canoe speed up exactly the same as the flow of the river, or will there be a variation? So if my paddling speed is 3 and the river speed is 1 would I then be traveling at 4 mph?"

That is the way navigation books present it at least. A one knot current will cut one knot from your paddling speed (unless you bear down and paddler harder of course). A one knot current in the direction you are going will add 1 knot to your boatspeed -- your speed relative to the riverbank, (but not to your speed relative to the river). If you can paddle at a speed of 4 knots and need to go 1 nautical mile upriver against a 1 knot current, it will take 20 minutes rather than the expected 15 -- because your speed is cut down to 3 knots.

(Though as posters above have intimated, either way, your speed relative to the rotation of the earth, or to the earth's rotation around the sun will be so slow as to be insignficant!)