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February 27th, 2012, 04:55 AM   #1
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Arithmetic Progression

Can someone help me please?

I have been set this question.

Water fills a tank at a rate of 150 litres during the first hour, 350 litres
during the second hour, 550 litres during the third hour and so on. Find the
number of hours necessary to fill a rectangular tank 16 m 9 m 9 m.

I have two workings out, could someone advise please?


a) Using Sn=n/2[2a+(n-1)d]
I get

1296=n/2[2x150+(n-1)x200]
I get n to be 3.36. 3.36 Hours.


b) Using Sn=n/2 (a+l)
I get

1296=4/2(150+l)
1296/2=648 648-150=498

So 1296=4/2(150+49 498/60=8.3 hours

Can anyone confirm either of these please?
I am led to believe that (a) is the correct method.
Thank you.
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February 27th, 2012, 07:38 AM   #2
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Re: Arithmetic Progression

Isn't one liter equal to .001 cubic meter ???
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February 27th, 2012, 07:51 AM   #3
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Use the first method. The tank capacity is 1296000 litres. Round calculated n down, then calculate flow rate for the next hour and hence calculate how much of that hour is needed.
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February 27th, 2012, 10:05 AM   #4
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Re: Arithmetic Progression

In case you're not sure why we need to go FLOOR(n), then portion:
(I'll use 1296 as you did)
Code:
1      150      150
2      350      500
3      550     1050
3.328  246     1296
1/750 * (1296 - 1050) = .328

Lower than your .36 result.
Doing it your way would be ok (I guess) if you assume the 750 speed is not "right away",
but increases from 550 to end up as an average of 750 during the 4th period.

Agree you guys?
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February 28th, 2012, 03:24 AM   #5
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Re:

Quote:
Originally Posted by skipjack
Use the first method. The tank capacity is 1296000 litres. Round calculated n down, then calculate flow rate for the next hour and hence calculate how much of that hour is needed.
Sorry for sounding dopey, could you explain that bit again please?
I have still worked out the same answer and am a bit confused.

Thank you all very much for your help with this.
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February 28th, 2012, 07:16 AM   #6
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This article explains why I used 1296000.
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February 28th, 2012, 07:40 AM   #7
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Re: Arithmetic Progression

Hi Skipjack.
I get that bit. The same answer of 3.6 presented itself following working out.which suggests about 3 hours and 36 mins.
Does that sound about right with your thoughts?
Thank you again.
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February 28th, 2012, 03:07 PM   #8
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As Denis indicated, it depends on whether the rates given are constant within each hour.
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