Lesson 127 of Doodles Do Algebra

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 $x/m=(b-x)/n$ 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!

First step is multiplying through by nm to “clear the fraction” and you get $nx=bm-mx$
Second step is moving the terms with the unknown, x, to one side of the equation and you get $nx+mx=bm$
And finally you divide both sides by the coefficient of x (in this case ‘n+m’) and you get $3/1(1+2)=3/3=1 mile$ 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.