Samantha ran on a fitness track for 20 min, and then walked for 15 min. Her running rate was 230 ft per minute faster than her walking rate. If she ran and walked a total of 16 comma 150 ft, how fast did she run?

  560 ft/min

Step-by-step explanation:

Let r represent Samantha's running rate in feet per minute. Then r-230 is her walking rate. We can use the relation ...

   distance = speed × time

to write an equation for the total distance Samantha went.

  20r + 15(r -230) = 16150

  35r - 3450 = 16150 . . . . eliminate parentheses, collect terms

  35r = 19600 . . . . . . . . . . add 3450

  r = 560 . . . . . . . . . . . . . . divide by the coefficient of r

Samantha ran 560 feet per minute.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.