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Read the posting on Sarin learns rate of change in school (Math Concept) to learn about concept of rate of change.
You can read the posting on Sarin learns Perimeter, Area and Volume in school(Math Concept) to learn the concept of volume.
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Upper primary school mathematics question UPQ257
The figure below shows 2 completely-filled tanks being emptied of the water from 2 different taps.
The taps at Tank A and Tank B were turned on at 7 am and 8.30 am respectively, until both tanks were completely empty. At 11 am, the water level in both the tanks was the same. At 12.30 pm, Tank B was completely empty and Tank A was only completely empty at 1 pm. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank A?
Using Portions of level per hour
The flow rates of both taps are constant and the tanks are in regular shapes.
The change of water levels of both tanks are proportional to their per hour flow rates.
So the water levels change according to the number of hours the taps turned on.
Draw the model water levels with respect to number of hours the taps turned on.
The water levels at 11am are same and can determine the relation of the flow rates of the two tanks
From the model
1 unit = 5cm
The height of Tank A = 5 × 9 = 45cm
The height (HA) of tank A = HA1 + HA2
The height (HB) of tank B = HB1 + HB2 = HA – 5
At 11 am, the water levels the same
HA2 = HB2
Volume of tank (V) = Height (H) × Base Area (A)
Flow rate (S) × Time = Volume (V)
For tank A
Set equation from 11am to 1pm (2h)
2SA = HA2 × AA è12SA = 6HA2 × AA
Set equation from 7am to 1pm (6h)
(HA1 + HA2) × AA = 6SA ==> (HA1 + HA2) × AA = 12SA
Slove the two equations
6HA2 = 2(HA1 + HA2) ==> 6HA2 = 2HA ==>8HA2 = 16HA
For tank B
Set equation from 11am to 12.30pm (1.5h)
1.5SB = HB2 × AB ==> 6SB = 4HB2 × AB
Set equation from 8.30am to 12.30pm (4h)
(HB1 + HB2) × AB = 4SB ==>1.5(HB1 + HB2) × AB = 6SB
Slove the two equations
4HB2 = 1.5(HB1 + HB2) ==> 8HB2 = 3(HB1 + HB2) = 3 (HA – 5) == > 8HB2 = 18(HA – 5)
16HA = 18HA – 90
2HA = 90
HA = 45cm
The height of tank A is 45cm