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 May 4th, 2018, 07:57 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 255 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, 08:15 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 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 08:39 PM.
May 4th, 2018, 08:19 PM   #3
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Quote:
 Originally Posted by v8archie Let $x$ ....e question.

 May 4th, 2018, 08:40 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 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 09:02 PM.
May 5th, 2018, 08:05 AM   #5
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Quote:
 Originally Posted by Ganesh Ujwal 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
Ganesh, that's another one of your silly problems;
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, 08:09 AM   #6
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Quote:
 Originally Posted by Ganesh Ujwal Ans: 75kmph
That isn't the correct answer for the problem you gave.

 May 5th, 2018, 08:56 AM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 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, 09:24 AM   #8
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 Originally Posted by v8archie I think it is. Denis had a time difference of 6 hours not 5 as given.
My "6 hours" was NOT the time difference:
it was simply using the given 450km distance
and the given 75kmph answer: 450/75 = 6;
in other words, the time taken by A.

May 5th, 2018, 09:39 AM   #9
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Beer soaked opinion follows.
Quote:
 Originally Posted by v8archie I haven't seen you post any answers. Or even any indication that you are thinking about the problems yourself.
I think it's about time we let Ganesh do his own homework without any help/comments/suggestions/hints.
I say we start ignoring his posts.
He clearly just wants someone else to do his job.
What say you friends?

 May 5th, 2018, 10:04 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,606 Thanks: 845 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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