Talk:Hotland/Puzzles/@comment-1643489-20170721040439

Say, regarding question 4 in Mettaton's Quiz Show. I decided I'd actually try to solve it. Here's my thought process, and I stuck to 3 decimals just like the answer.


 * deep breath*

Train A moves at 124.7 mph, so it's 60 minutes for every 124.7 miles, which is 2.078 miles a minute, which means it takes 121.492 minutes for Train A to reach Station B. Train B moves at 253.5 mph, so it's 60 minutes for every 253.5 miles, which is 4.225 miles a minute,  which   means it'll take 59.763 minutes for Train B to reach Station A.

Next. Imagine a (X,Y) graph, Y is distance, X is time. Station A's location is (0,0), Station B's location is (0, 252.5). Train A ends at (121.492,252.5), and Train B ends at (59.763,0).

For Train B, (0, 252.5) and (59.763, 0) are the two points, so the equation is ?X + ?Y = 59.763. Determine Y's coefficient. ?(0) + ?(252.5) = 59.763, so ? * 252.5 = 59.763, so ? = 59.763 / 252.5, means the coefficient is 0.236. Determine X's coefficient. ?(59.763) + ?(0) = 59.763, so ?(59.763) = 59.763. Makes X's coefficient 1. So Train B's equation is X + 0.237Y = 59.763.

For Train A, (0,0) and (121.492,252.5) are the two points, so the equation is ?X - ?Y = 0, which is also ?X = ?Y. Use end time and distance for Train A, so (?)121.492 = (?)252.5. I need X to be 1, so equation will be 121.492 = (?)252.5, so 121.492 / 252.5 = ?. Y's coefficient will be 0.481, therefore Train B's equation is X - 0.481Y = 0.

Train equations are therefore X + 0.237Y = 59.763 and X - 0.481Y = 0. Y is easier to determine, so remove X, and get 0.718Y = 59.763. Y is therefore 59.763 / 0.718, which is 83.254. Now with Y, determine X using X - 0.481Y = 0, or X = 0.481Y. That means X = 0.481 * 83.254, which is 40.058.

Meeting point of two equations is therefore (40.058, 83.254), which means trains pass each other 83.254 miles from Station A 40.058 minutes from when they depart at 10:00 AM. 10:08 in the equation, so subtract 8 minutes and get 32.058 as the answer.