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You are not logged in. #1 20120712 23:16:21
The Two Trains and How FastHere's my approach to it but I can't find what's wrong: Let time taken by the first train TO COMPLETE THE WHOLE JOURNEY be t1 Let time taken by the second train TO COMPLETE THE WHOLE JOURNEY be t2 Let the distance between London and Liverpool be d Let the time when they had met each other be f Now: Because at the moment of passing each other the distance both trains have covered add up to d Because Train1 takes one hour more after the passing each other moment Because Train2 takes four hours more after the passing each other moment I shall call the above Equation 1, 2 & 3 respectively From Equation 2: or or From Equation 3: or or Therefore, we can say that: Putting t2 = (t1 + 3) and f = (t1  1) in Equation 1: After fooling around with it you get: Now according to the brute force method of Quadratic equations, I get: and Ultimately we get the following things: What are the mistakes(if any), I have commited in my above calculations? Now the most important thing: The puzzle told us to find how much faster is one train running than the other and the answer given in the book is this: How can I come to the conclusion in the answer? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20120712 23:55:00
Re: The Two Trains and How FastHi Agnishom; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20120713 04:23:10
Re: The Two Trains and How Fasthi Agnishom so t1 = 3 not 3d. (d is a distance so how could the time be equal to 3 x it ?) implies t2 = 6 So the slow train is taking twice as long => twice as fast. As for your method, I think you have over complicated it. (i) I always like to have a distance / time graph as it helps me to see what unknowns I have (ii) Don't introduce more unknowns than needed as it just makes the algebra worse. So I had time to crossover = t, distances covered to this point c and d. Then and Divide one equation by the other and both c and d are eliminated giving So the times for the whole journey are 2 + 4 and 2 + 1 Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #4 20120713 21:56:48
Re: The Two Trains and How FastHi Bob, Please explain the above
My Answer 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #5 20120713 22:38:14
Re: The Two Trains and How FastHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20120714 06:44:21
Re: The Two Trains and How Fasthi Agnishom and Stefy, so so either d = 0 or t1 +1 = 0 or t1 3 = 0 As we know d isn't zero and the negative doesn't fit the problem we can conclude t1 = 3. The 'd's have gone from the problem. How did I get d/t = c/1 ? That's distance / time = speed for each part of the journey (speed is the same for both parts) Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20120714 06:46:25
Re: The Two Trains and How FastYes, he didn't solve it properly. I think he put only 2 instead of 2a in the quadratic formula. A common error. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20120714 07:06:28
Re: The Two Trains and How FastMaybe. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #9 20120714 07:10:15
Re: The Two Trains and How FastBut if the expression can be factorized then the quadratic formula won't have any nasty decimals. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20120714 07:19:46
Re: The Two Trains and How FastArrhhh, you spotted the flaw in my argument. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #11 20120714 07:23:50
Re: The Two Trains and How FastHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20120714 07:37:10
Re: The Two Trains and How FastYou do it your way and I'll do it mine. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #13 20120714 07:43:29
Re: The Two Trains and How FastThat we agree on. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20120714 15:07:36
Re: The Two Trains and How Fast
Yes thats true 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #15 20120714 20:45:47
Re: The Two Trains and How FastHi Agnishom; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #16 20120722 14:36:29
Re: The Two Trains and How FastOho! Really? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #17 20120722 14:37:41
Re: The Two Trains and How FastOf course. I must've forgotten the 'a' at least 40 times. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #18 20120722 16:13:32
Re: The Two Trains and How Fast40 times or 10^40 times? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20120723 00:15:07
Re: The Two Trains and How FastAt least 40 times. 10^40 is too much, though. I give an upper bound of 1000. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #20 20120726 23:02:05
Re: The Two Trains and How Fast40 times out of a total of how many? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #21 20120726 23:50:42
Re: The Two Trains and How FastHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #22 20120727 00:24:22
Re: The Two Trains and How FastWhat is "anonimnystefy constant"? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #23 20120727 03:43:37
Re: The Two Trains and How FastIt has a numerical value of 10^40. Other than that I do not know much about it. It first showed up in a thread where you were given 20 guesses to guess someone's occupation and identity. He needed or took more guesses, hence the anonimnystefy constant. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #24 20120727 04:00:21
Re: The Two Trains and How Fastbobbym is the one to propose that the number of guesses for we should be 10^40. But I grabbed the name for it before he could. But, I recently coined the term bobbym constant for the number 123456787654321. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #25 20120727 04:03:24
Re: The Two Trains and How FastI already have a constant named after me. There is a rule in math. One constant per person. There are no exceptions. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 