This is for understanding rates. Let me explain. In the top half, Scratch and Gobo are going in the same direction. Scratch is going at a rate of 60 pixels per second, and Gobo is going at a rate of 40 pixels per second. The space between them is 50 pixels wide. Scratch will catch up to Gobo in 2.5 seconds. In the bottom half, it's the same, but Gobo is not moving, and Scratch is going at a rate of 20 pixels per second. The distance between the two is still the same. Scratch will still catch up to Gobo in 2.5 seconds. But maybe you're thinking, "What's the relationship?" Well, look closely at these rates. 60 - 40 = 20. 40 - 40 = 0. So we changed the rates by subtracting 40 from both sides. This can be explained using variables. Set x to the number of seconds it takes for Scratch to catch up to Gobo. Our equation is 60x - 50 = 40x, because Scratch has to travel 50 pixels first. Subtract 40x from both sides. 20x - 50 = 0 Add 50 to both sides. 20x = 50 Divide both sides by 20. x = 2.5 That's the same answer we got previously. This random subtracting of rates doesn't change our answer, because we subtract by the same amounts, to both rates. And that's all there is to it!
Credit to spaghetti, for being delicious.
