Every now and then I like to pull out an old puzzler that I haven't used lately to illustrate the magic and wonder of mathematics in the solution of "neat" or interesting problems. There is a lot of fun in doing this--not only does it offer a glimpse of the power of mathematics to get to the heart of a problem, but it also offers the challenge to others to refine a solution; it even continues to amaze some who do not immediately accept the proferred solution.
Such a problem is the following:
Suppose two ships leave a pier on a river (the Mississippi??) at exactly the same instant, one traveling upstream and one traveling downstream at exactly the same still-water rate. At the exact instant of departure, a life jacket falls from one of the ships and begins floating downstream. After one hour, the ships instantly turn around and begin sailing back in their respective opposite directions. Which one of the ships will meet the life jacket first?
A problem without numbers! What a great way to illustrate the power of mathematical thinking. Do we care about the speed of the ships? The speed of the current? The brand name of the life preserver?
Strictly using variables to represent things in the problem, we can establish enough relationships to solve the problem. This is an excellent exercise for your algebra students.