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Thread ID: 95701 2008-12-14 23:48:00 Maths Problem Dally (6292) PC World Chat
Post ID Timestamp Content User
729116 2008-12-15 04:39:00 Gosh MushHead, I wish I could have done that. Never was much good at maths at school, or after, for that matter. :thumbs: Richard (739)
729117 2008-12-15 05:19:00 OK then, to clarify:

let X be our pool size, Vp & Vs the swim speeds of Phelps & Smith respectively.

We have 2 points in time that we know - when the swimmers cross each other.


t1 = (X - 35)/Vp = 35/Vs

and at the other end (I'm assuming Smith has swum a length, rested 60s, then started back, rather than Phelps overtaking him on Smith's first length)


t2 = (2X - 15)/Vp + 60 = (X + 15)/Vs + 60

from these 2 relationships we can say


Vp = (X - 35)Vs/35 (from t1)

We substitute this into the t2 equation (after cancelling out the 60s on each side):


(2X - 15) = (X + 15)
((X-35)Vs/35) Vs

Now we can cancel out Vs & reorganise to get:


35(2X - 15) = (X + 15)(X - 35)

or


70X - 525 = X^2 - 20X - 525

this reduces down to


90X = X^2

so X=90.

What he said :D 		Marnie (4574)
729118 2008-12-15 05:41:00 I think this proves that computer geeks are not always good at maths:P Blam (54)
729119 2008-12-15 09:16:00 Very good Mushead - There is also a beautiful intuitive solution

When they first cross their combined distance equals one length. When they cross again their combined distance equals three lengths therefore JS has swum three times 35m which is 105m but he has swum one length plus 15m - Length of pool 90m

That is indeed a beautiful solution.

I have always been good at solving these sorts of problems the traditional ways such as simultaneous equations (not meaning to sound conceited) but I always struggle to spot the much simpler solutions like the one you provided. Thanks for posting this. 		roddy_boy (4115)
729120 2008-12-15 09:55:00 That is indeed a beautiful solution.

I have always been good at solving these sorts of problems the traditional ways such as simultaneous equations (not meaning to sound conceited) but I always struggle to spot the much simpler solutions like the one you provided. Thanks for posting this.

Um, sorry but "simpler solution"? Please tell me that's a typo lol, cuz I really don't see how any of that is near simple 		--Wolf-- (128)
729121 2008-12-15 10:48:00 Simpler in the sense that it doesn't require very much "maths" at all.

I was responding to Dally in my post if you missed that btw. 		roddy_boy (4115)
729122 2008-12-15 19:39:00 I'm with roddy - I always jump to the old equation-based solution before trying to come up with an "intuitive" solution.

I find it interesting that, when doing the (long-winded) maths, everything cancels out just so to leave a solution, whereas at 1st glance it looks like you've got 2 equations for 3 unknowns, which would make it unsolvable. This matched my initial impression that there was information missing, because you'd normally think that the swimmer's speed would come into it, when in fact it doesn't (note there's no way of working out the speeds, just the ratio between them). 		MushHead (10626)
729123 2008-12-16 03:06:00 MushHead - Construct the equations is also the first approach I would take. I was fortunate to have a brilliant, if somewhat eccentric, maths teacher. We were about 12 months ahead of the syllabus so he liked us to bring maths problems to class and equations were always the first approach although he would sometimes throw in an intuitive solution. Sadly I dont think he would have survived in modern system of education. Dally (6292)
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