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February 27th, 2012, 04:55 AM  #1 
Newbie Joined: Feb 2012 Posts: 8 Thanks: 0  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+(n1)d] I get 1296=n/2[2x150+(n1)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 648150=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. 
February 27th, 2012, 07:38 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Arithmetic Progression
Isn't one liter equal to .001 cubic meter ???

February 27th, 2012, 07:51 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
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.

February 27th, 2012, 10:05 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  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 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? 
February 28th, 2012, 03:24 AM  #5  
Newbie Joined: Feb 2012 Posts: 8 Thanks: 0  Re: Quote:
I have still worked out the same answer and am a bit confused. Thank you all very much for your help with this.  
February 28th, 2012, 07:16 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216  This article explains why I used 1296000.

February 28th, 2012, 07:40 AM  #7 
Newbie Joined: Feb 2012 Posts: 8 Thanks: 0  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. 
February 28th, 2012, 03:07 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
As Denis indicated, it depends on whether the rates given are constant within each hour.


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