Today DoodlePig takes your child through the problem of the two messengers running at each other and answers the age-old question of, “When will they meet?”

The work your child does today is first following through the explanation and logic of the problem, and next finishing the problem by solving for x, or the distance the first messenger travels.

If you want to take the problem further with your child, you can work out the answer when both messengers are traveling at the same speed towards each other. In that case the m and the n terms are the same and cancel out of the equation.

This is the problem that has plagued crowds and crowds of high school and first year college students in physics class. And if you explain it clearly and make certain your child understands it, then he will be set for life. That is an effort well worth the time to expend!

Download Lesson 127 of Doodles Do Algebra HERE

Answer:

First step is multiplying through by nm to “clear the fraction” and you get

Second step is moving the terms with the unknown, x, to one side of the equation and you get

And finally you divide both sides by the coefficient of x (in this case ‘n+m’) and you get to th point that they meet. That means that the second messenger has traveled 2 miles, since the total is 3 miles between them at the start.

It is really not hard, unless confusion and dread was sewn into your head by a high school teacher who was amazed that women and girls could form a complete thought since they were, after all, women and was thus completely convinced that you could never do algebra like this. Then you will be left with a life-long sense that this kind of problem is just to complicated. From experience, you can avoid passing this badness onto your children if you walk them through the steps carefully and slowly. Your kids will grow up thinking it is all quite easy – and that is a great thing!