
By: tchtby (offline) Thursday, September 19 2013 @ 01:35 AM CDT (Read 1466 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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Registered: 10/15/12 Posts: 13





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

Active Member
Registered: 04/21/11 Posts: 623





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



tchtby 

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Registered: 10/15/12 Posts: 13





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



tchtby 

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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?

Newbie
Registered: 10/15/12 Posts: 13





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

Active Member
Registered: 04/21/11 Posts: 623



