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Results 1 to 13 of 13
Thread: river crossing
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30th May 2011, 07:33 PM #1
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river crossing
Two polluting carbon emitting gas guzzling power boats start at the same time from opposite side of the polluted Marrickville River, that is not ebbing or flowing, being full of garbage.
They travel at constant speed at rights angles to the river banks, but one is faster than the other.
They pass at a point 720 metres from the nearest shore.
Both boats remain at the wharf for 10 minutes while they fill with more polluting petroleum before starting back.
On the return trip, they met 400 metres from the other shore.
Once the reach the shore again, they are stoned to death by green Councillors.
How wide is the river?
Greg
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30th May 2011, 11:34 PM #2
Does it matter? Their dead!
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30th May 2011, 11:40 PM #3
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31st May 2011, 05:42 PM #4
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sorry.
Try this:
Let x be the river width.
On the first trip the ratios of distances travelled by the 2 boats is x-720:720
On the second trip it is:
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31st May 2011, 06:17 PM #5
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31st May 2011, 06:58 PM #6
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And
Those ratios are equal.
x-720/720 = 2x-400/x+400
(x-720)(x+400) = 720(2x-400)
x2-720x+400x-288000 = 1440x-288000
x2-320x-1440x = 0
x(x-1760) = 0
So the answer is:
Thanks
Greg
ps x2 is x 'squared', I can't make the machine type the correct symbol
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31st May 2011, 07:01 PM #7
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31st May 2011, 07:05 PM #8
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After 15 minutes or so trying to remember how to solve these, I instead remembered that I hate maths so instead went and looked at pretty tools I can't afford. I'm feeling much better about not knowing the answer now!
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31st May 2011, 07:35 PM #9
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31st May 2011, 07:37 PM #10
I was a bit worried about the 10min stop by the boats but as it turned out it didn't matter in the end.
Visit my website at www.myFineWoodWork.com
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31st May 2011, 07:43 PM #11
Let x be the width
Let v1 be the velocity faster boat
Let v2 be the velocity slower boat
Let T be the time taken
The boats first meet:
v1/v2 = (x - 720) / 720
Second meet:
v1 = (2x - 400) / (T - 10)
v2 = (x + 400) / (T - 10)
v1/v2 = (2x - 400) / (x + 400)
Therefore (x - 720) / 720 = (2x - 400) / (x + 400)
x = 1760Visit my website at www.myFineWoodWork.com
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31st May 2011, 07:47 PM #12
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yards
When this was first mooted, it was in yards, and as we know who are post 1963...
1760 yards equals..... 1........
Good work Scott ( as usual...).
Greg
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20th September 2012, 07:55 AM #13
1760 yards is a mile. Easy!!
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