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solvingmaths
 Post subject: Metting point of A and B
PostPosted: Thu, 31 May 2012 14:22:30 UTC 
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First off - this is not homework, this is voluntary work to get ready for a test I'm having in a week.

"A motorcyclist is in a city A, and he is able to go to a city B in 3 hours. Another motorcyclist is in city B, and he is able to get to a city A in 2 hours. They both leave the towns at the same time. When will they meet?"

I was able to solve such exercises before, but now I'm having trouble with it. I've tried taking a random number and calculating the times, but obviously the answer was wrong.
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outermeasure
 Post subject: Re: Metting point of A and B
PostPosted: Thu, 31 May 2012 14:46:23 UTC 
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Topic moved from Calculus to Algebra.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: Metting point of A and B
PostPosted: Thu, 31 May 2012 16:54:16 UTC 
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solvingmaths wrote:
First off - this is not homework, this is voluntary work to get ready for a test I'm having in a week.

"A motorcyclist is in a city A, and he is able to go to a city B in 3 hours. Another motorcyclist is in city B, and he is able to get to a city A in 2 hours. They both leave the towns at the same time. When will they meet?"

I was able to solve such exercises before, but now I'm having trouble with it. I've tried taking a random number and calculating the times, but obviously the answer was wrong.


Can you show us what you tried? It's impossible to see where the trouble is otherwise. :)

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aswoods
 Post subject: Re: Metting point of A and B
PostPosted: Sun, 10 Jun 2012 13:13:46 UTC 
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Draw a diagram. Assuming that they travel at constant speeds in opposite directions on the same road, then when they meet, the faster motorcyclist will have covered 1½ times the distance that the slower motorcyclist has covered. That means that the slower motorcyclist has covered a fraction p/q of the total distance, which must have taken p/q of three hours.
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alstat
 Post subject: Re: Metting point of A and B
PostPosted: Mon, 11 Jun 2012 06:54:17 UTC 
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Use D = RT, plus the fact that R_1 = \frac{2}{3}R_2.

Spoiler:
Then D = (R_1 + R_2)\cdot T = R_2\cdot2

or \frac{5}{3}T\cdot R_2 = 2R_2 \rightarrow T = \frac{6}{5} or 1:12.
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