illustrate a method for solving distance problems that avoids using rational equations
As a high school teacher, I was often amazed at the creativity of my students when it came to solving word problems in clever ways. One student showed me how to avoid using a rational equation when solving certain kinds of distance problems. she would go to great lengths to avoid the rational equation - which shows the extent of her dislike for them. So, thanks to that clever girl, I have this method to share with you.
This is not to say that solving rational equations doesn't have its place in algebra - that technique is useful in many situations. But, I offer this alternative approach just as another tool in your box of tools.
The three problems I present progress in difficulty - by the time you get to the last one, you should feel fairly comfortable with the technique.
Zebras run faster than elephants - it's true. This illustration shows you how to find the speed of each animal and avoid using a rational equation.
The two cars are going the same distance but at different rates - again we avoid a rational equation and determine the speed.
In this problem all three elements of the set-up are different - distances, rates and times. The resulting equation is still quadratic but there is another twist to it - and a clever trick to avoiding the rational equation.
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