Eliz,

Thanks for taking a look. I almost gave up on this, but I just couldn't. I decided to experiment by creating a similar problem in which the rates were known, the time was known, and the requirement was to find the rate at which the two jets were separating at a given time. I contrived it to work out. Then I tried to solve the same problem except changing the unknown to "when will the two jets be separating at such and such a rate?" It was just as impossible as the above!

As a result, my hypothesis is that the

method attempted, as described in the prior post,

is not valid because it involves making time a variable in a context in which quantities are changing with respect to time. IOW, we can't mix

with

. At least, I don't know of a way to do that.

I went back to the original problem and experimented. Since 640 and 600 are multiples of 4 and the difference in the times is 1/4 hour, I figured, let's see where the two jets are every 15 minutes once the second jet passes over the town.

Click on link for spreadsheet:

http://spreadsheets.google.com/pub?key=r9P9eSgXFuOShFXnCzElu8w&hl=en. One thing I noticed was how the changes in rate of separation decreased over the succession of 15-minute intervals. I thought that was interesting.

I had noticed with other problems of this type, where, e.g. the unknown is the rate of one of the vehicles, a rate of separation or approach, or a distance, it turns out to be contrived to involve a convenient Pythagorean triple (extended to rationals with terminating decimals). When I was working the above out and came to the 1:00 p.m. entry, I realized immediately that the x-distance = 600 and y-distance = 800 were a Pythagorean triple in the making and that the problem would have to be so contrived to make the 872 work out.

So, getting back to

and

, so

, and

Not exactly a "plug it in and crank it out" solution. If you (or anyone out there) know of a more methodical approach for a related rate problem with this type of requirement and conditions, I'd be very interested in learning. I hope that these posts are contributing something worthwhile.