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Friday, August 18 2017 @ 07:48 AM CDT
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 p6 math
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By: tchtby (offline)  Thursday, September 19 2013 @ 01:35 AM CDT (Read 1477 times)  
tchtby

A rectangular tank measuring 250 cm by 40 cm by 100 cm was 1/4 filled with water.
Tap A was then fitted and had water flowing into the tank at a rate of 5 litres per min and Tap B had water drained out from the tank at a rate of 2 litres per min.
Tap A was turned on for 3 minutes and then it was turned off.
Immediately after tap A was turned off, tap B was turned on for 3 minutes and then it was turned off.
The 2 steps were repeated until the tank was completely filled without water overflowing.
How long did it take for the tank to be filled?

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By: echeewh (offline)  Thursday, September 19 2013 @ 06:19 AM CDT  
echeewh

hey <tchtby>


//Updated 19/9/13 23 55
Thanks for your <Answerkey>
//



Following is my worked solution:

Vol of water (1/4 filled)
= 250 × 40 × 100 × (1/4)
= 250000 cm3
= 250 litres

Inflow of water for 3 mins (when A turned on)
= 5 × 3 = 15 litres

Outflow of water for 3 mins (when B turned on)
= 2 × 3 = 6 litres

Net inflow of water after 6 mins
= 15 - 6 = 9 litres

Capacity of tank
= 250 × 4
= 1000 litres

Thus, 750 litres are required to fill tank up to the brim.

750 ÷ 9 = 83 (R 3 litres)

Note:
Have to use 82 groups as this will fill up 738 litres {82 × 9}. Cannot use the last group of 83 as the first 3 mins inflow of water will add 15 litres causing an overflow {738 + 15 = 753}.

Thus, time taken = 82 × 6 = 492 mins

To fill up tank with remaining 12 litres {750 - 738},
time taken (inflow) = 12 ÷ 5 = 2 2/5 mins

Hence, total time taken to fill up tank
= 492 + 2 2/5
= 494 2/5 mins
= 8 hrs 14 2/5 mins


========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

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By: tchtby (offline)  Thursday, September 19 2013 @ 07:57 AM CDT  
tchtby

but ans is 494 2/5 min

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By: tchtby (offline)  Thursday, September 19 2013 @ 08:27 PM CDT  
tchtby

thks a lot

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By: tchtby (offline)  Friday, September 20 2013 @ 04:50 AM CDT  
tchtby

hi

i would like to ask if there are 82 fill cycle which will fill up 82 x 9 = 738 litre. So the next fill cycle tapA will fill another 15 litres so 738 + 15 = 753(overflow). If there are 83 fill cycles which will fill up 83 x 9 = 747 litres. So the next fill cycle tapA will fill another 15 litres and it will overflow too. Can you please enlighten me?

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By: echeewh (offline)  Friday, September 20 2013 @ 02:05 PM CDT  
echeewh

Hi <

Pls find my clarification below:

Looks like you don't get to understand my note (explanation) on why it has to stop after repeating both inflow + outflow processes (3 mins of each) for 82 times.

Cannot repeat such step for the 83rd time as the 1st 3 mins of inflow (15 litres) will cause an overflow.

That is why we repeat only the inflow process accordingly (i.e. for only 2 2/5 mins) to fill up tank to the brim (without overflow), afterwhich Tap A was turned off.

Trust this helps.

Thank you and all the best in your PSLE,
Edward


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