Rate of Water Flow Question (Involving Volume Dimensions)
The primary goal of this math revision note is to enhance your child’s proficiency in solving rate of water flow questions involving volume dimensions and proportionate heights.
These questions assess your child’s understanding of rate and volume.
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Rate of Water Flow (Volume Dimension) Question 1
The figure shows taps A and B with two empty tanks A and B.
Both taps are turned on at the same time.
Water flowed from tap A into tank A at a rate of 5 litres per minute.
(a) What should the rate of flow of water be from tap B such that the height of water is the same for both tanks after some time?
(b) What should the rate of flow of water be from tap B such that the height of water in tank A is twice that of tank B after some time?
Solutions for (a)
Base area of Tank A = 70 cm × 50 cm = 3500 cm2
Base area of Tank B = 84 cm × 50 cm = 4200 cm2
Since the question requires the height of water to be the same, we can set this height as 1u.
For every 5 units of water in Tank A, there must be 6 units of water in Tank B in order for the height of water in both tanks to be the same.
The rate of water flow of Tap A is 5 litres per minute.
This means that in the 1-minute time frame, 5 litres of water have entered Tank A. For the water in Tank B to have the same height, there should be 6 litres of water that have entered Tank B in this 1-minute time frame.
5 u = 5 litres per minute
1 u = 1 litres per minute
6 u = 6 litres per minute (Ans)
Solutions for (b)
Since the question requires the height of water in tank A to be twice of that in tank B, we can set the height of water in Tank A to be 2u while the height of water in tank B to be 1u.
5 u = 5 litres per minute
3 u = 3 litres per minute (Ans)
Alternative solutions for (b)
From (a), we know that for the water in both tanks to have the same height, Tap B’s rate has to be 6 litres per minute while Tap A’s rate is 5 litres per minute.
So, for the water in Tank A to have double the height of the water in Tank B, Tap B just need to produce half as fast as before or half as productive as before.
Hence the rate of Tap B = 6 ÷ 2
= 3 litres per minute (Ans)
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