What we are doing in algebra is very interesting. This past week we have worked on how to find out when and where two cars will hit each other when they are going toward each other at different speeds. Or also when one car will catch up to the other when they start at different points, and the one in the back is faster. So I am going to explain how to solve these kinds of problems. First of all you need to find out the speed of each car, and also their starting point. Then you can get the equations for each line.
So here is an example of two equations: y= 40x+10, y= -25x+400. So the way you start is by putting the two equations together, and you do that by changing it to 40x+10= -25x+400, since those two equal each other. You know that because they both equal "y" so they must equal each other. So once you have this you just have to solve for "x". You end up getting x=6. Then you plug 6 in for "x" in either of the two equations. It doesn't matter which one because they are equal to each other. Once you do that you solve the problem to get what "y" equals. In this case "y" equals 250. So now you have the coordinates of the point where these two cars will hit each other: at (6,250).
This is how you get the coordinates to where two objects will hit each other or one catch up to the other. My example was of two cars hitting, but this works for the catching up as well. This method will work every time.
So here is an example of two equations: y= 40x+10, y= -25x+400. So the way you start is by putting the two equations together, and you do that by changing it to 40x+10= -25x+400, since those two equal each other. You know that because they both equal "y" so they must equal each other. So once you have this you just have to solve for "x". You end up getting x=6. Then you plug 6 in for "x" in either of the two equations. It doesn't matter which one because they are equal to each other. Once you do that you solve the problem to get what "y" equals. In this case "y" equals 250. So now you have the coordinates of the point where these two cars will hit each other: at (6,250).
This is how you get the coordinates to where two objects will hit each other or one catch up to the other. My example was of two cars hitting, but this works for the catching up as well. This method will work every time.
RSS Feed