Let A, M, and w represent Angelo's distance per week, Marc's distance per week, and the number of weeks of this regimen, respectively. .. A = w +7 . . . . . . . Angelo's distance goes up 1 mile/week each week .. M = 2w +4 . . . . . Marc's distance goes up 2 miles/week each week
a) A = M .. w +7 = 2w +4 .. 3 = w . . . . . . . . . . subtract w+4
After 3 weeks Angelo and Marc will be running the same distance.
b) A = M = 3+7 = 2*3+4 = 10
That distance will be 10 miles per week.
_____ This problem can be a little confusing because "miles per week" is a rate, and we're talking about the rate of increase of that rate: 1 or 2 miles per week per week. It might be easier to think of the numbers as "weekly distance", rather than "miles per week".
The negative in front of the second bracket means that it's times by -1 so each of their signs switches: 3m^2+2n-m^2-2n Add like terms 2m^2 the 2n cancels out
