Most-efficient inexpensive way to speed/slow video track to sync with audio track? My machines are a few Android tablets (not the newest, but not too old either) as well as a Mac running OS X 10.9.5 (not about to upgrade the OS - long and irrelevant story why). Sometimes I do a presentation where I record separately the video track and the audio track - and then selectively speed-and-slow parts of the video track to sync with the audio --- thereby producing something similar to whiteboard animation.

Here's my question. The current way I do the speeding-up and slowing-down is through iMovie -- where I load the video, strip the audio that comes with me (which is just the sounds that are in the room at the time) load the audio that it is meant to go with --- and then I split the video clip at the right places, and for each segment, adjust the speed manually, thereby getting the video to sync with the audio. It's a slightly tedious process --- and I'd like something a tad more efficient. Say, something that would allow me to select key points where I map the audio track to a corresponding key point in the video track -- and maybe let the program then automatically speed-up and slow-down the video segments between those key-points so that things sync. Would make the process much less tedious.

Here's the thing though -- I am on a very limited budget -- and therefore, if the only options for something like this are too expensive, I probably will then just go on doing it the way I'm currently doing it through iMovie (which is tedious - but gets the job done). I can spend a little money, but something expensive is just out-of-the-question for me - and will remain so for a while it looks like. I'd like to have more money to spend on expensive tools (and if I had such money, I would have been using FinalCut Pro rather than iMovie for example) but the reality of the situation is that I don't have much money to spend.

So --- any suggestions what tool I can use to more-easily speed-slow the segments of the video track to sync with the audio track?
Well you could download a trial 30 day copy of the legacy version of Adobe After Effects CS6. It allows a full unrestricted 30 day install trial. 

From there, you could take your footage in, place the master clip in a composition, and instead of cutting it, use the the time warp feature, which will give you smooth keyframes where you can adjust up the speed to X, then place a keyframe if you notice it begin to slip, and set a keyframe to slow it down a bit. This will provide ramping, which basically "cuts" the clip in half over and over again, and does all the math for you, to make the smooth changes in speed. Then render it out. Premiere might also have that function- it's also included in the CS6 Production Premium Bundle, google the download link, and you can install and try for 30 days without purchase.