Two water tanks sit side by side on a farm.
Tank A has a capacity of 1000 litres and is full. It is being emptied at a constant rate of 60 litres per minute.
At the same time, Tank B is empty and is being filled at a constant rate of 40 litres per minute.
Let \(V\) = volume of water in litres, and
\(t\) = time in minutes.
- The equation \(V=1000-60t\) models the volume of water in Tank A.
- Write an equation to model the volume of water in Tank B. (1 mark)
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- Complete the table below and use the values to graph the volume of water in Tank A and Tank B on the grid below. (3 marks)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Tank A} & \ \ \ \ \ \ \ \ & 880 & 760 & 640 & 520 & 400 & 280 \\ \hline \text{Tank B} & 0 & \ \ \ \ \ \ \ \ \ & 160 & 240 & 320 & 400 & \ \ \ \ \ \ \ \ \\ \hline \end{array}\)
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- After how many minutes do both tanks contain the same volume of water? (1 mark)
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- What is the volume of water in each tank at this time? (1 mark)
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a. \(V=40t\)
b. \(\text{Table of values:}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Tank A} & 1000 & 880 & 760 & 640 & 520 & 400 & 280 \\ \hline \text{Tank B} & 0 & 80 & 160 & 240 & 320 & 400 & 480 \\ \hline \end{array}\)
c. \(10\ \text{minutes}\)
d. \(400\ \text{litres}\)
a. \(V=40t\)
b. \(\text{Table of values:}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Tank A} & 1000 & 880 & 760 & 640 & 520 & 400 & 280 \\ \hline \text{Tank B} & 0 & 80 & 160 & 240 & 320 & 400 & 480 \\ \hline \end{array}\)
c. \(\text{From the graph, the lines intersect at }\ t=10.\)
\(\therefore\ \text{Both tanks contain the same volume after 10 minutes}\)
d. \(\text{Method 1: Graphically}\)
\(\text{From the graph, when }\ t=10,\ \text{the volume in both tanks = 400 litres}\)
\(\text{Method 2: Algebraically}\)
\(\text{When }\ t=10:\)
\(\text{Tank A volume:}\ \ V=1000-60\times10=400\ \text{L}\)
\(\text{Tank B volume:}\ \ V=40\times10=400\ \text{L}\ \checkmark\)
\(\therefore\ \text{Each tank contains } 400\ \text{litres}\)