May 4th, 2018, 08:57 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  What is the speed of train A?
Two cities P and Q are separated by a distance of 450km Train A starts from city P to reach city Q five hours after train B starts from city P. Train A runs 15kmph faster than train B. Both the trains reach city Q at the same time. What is the speed of train A? Ans: 75kmph How to solve this problem? 
May 4th, 2018, 09:15 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2561 Math Focus: Mainly analysis and algebra 
Let $x$ be the speed of train A. Write an equation using the given information that describes the fact that both trains arrive at the same time. You can also just write the equation with many variables, and then substitute all but $x$ out using the information in the question. Last edited by v8archie; May 4th, 2018 at 09:39 PM. 
May 4th, 2018, 09:19 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
May 4th, 2018, 09:40 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2561 Math Focus: Mainly analysis and algebra 
I haven't seen you post any answers. Or even any indication that you are thinking about the problems yourself. Let $t_a$ be the time train A takes to travel from P to Q. Let $t_b$ be the time train B takes to travel from P to Q. Then $$5+t_a = t_b$$ But $$\text{average speed} = \frac{\text{distance}}{\text{time}} \implies \text{time} = \frac{\text{distance}}{\text{average speed}}$$ Can you finish? Last edited by v8archie; May 4th, 2018 at 10:02 PM. 
May 5th, 2018, 09:05 AM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,799 Thanks: 970  Quote:
are you too busy or tired to at least check? Let A leave P at 1pm: then A arrives at Q at 7pm (450/75 = 6 hours). So 5 hours before 7pm is 2pm: so B leaves P at 2pm. B's speed is 60kmph (15 less than A); so takes B 450/60 = 7.5 hours So B arrives at Q at 9.5pm So we have A arriving at 7pm and B arriving at 9.5pm: that's NOT at same time. Something is wrong: the problem itself, or the given answer of 75 kmph.  
May 5th, 2018, 09:09 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,104 Thanks: 1907  
May 5th, 2018, 09:56 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2561 Math Focus: Mainly analysis and algebra 
I think it is. Denis had a time difference of 6 hours not 5 as given.

May 5th, 2018, 10:24 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,799 Thanks: 970  
May 5th, 2018, 10:39 AM  #9  
Senior Member Joined: May 2008 Posts: 298 Thanks: 81  Beer soaked opinion follows. Quote:
I say we start ignoring his posts. He clearly just wants someone else to do his job. What say you friends?  
May 5th, 2018, 11:04 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,799 Thanks: 970 
Thou art mean, Sir Jonah...but I agree! But I'm now hooked on this one: I now see the obvious error in problem: B travels 15 kmph FASTER than A, not 15 kmph slower. [P]A@75(1pm)...................450................... >7pm[Q] [P]B@90(2pm)...................450................... >7pm[Q] Amen! 

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