Linear Graphs and Its Applications - Linear Graphs in Real Life Problems

Two containers are filled from separate taps. Container A initially contains \(12\) litres of water and receives \(3\) litres per minute. The volume of water in Container B is modelled by \[V=24+1.5t,\] where \(V\) is the volume in litres and \(t\) is the time in minutes after both taps are turned on.
Both containers have a capacity of \(80\) litres.

1. Write an equation for the volume of water in Container \(A\). Hence find its volume after \(6\) minutes.

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2. Explain what the numbers \(24\) and \(1.5\) represent in the equation for Container \(B\).

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3. On graph paper, draw the graphs for both containers for \(0\leq t\leq16\). Use a horizontal axis from \(0\) to \(16\) minutes and a vertical axis from \(0\) to \(80\) litres.

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4. Use your graphs to find when the containers contain the same volume of water. State this volume.

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5. A student says, “Container \(B\) started with more water, so it will always contain more water.” Explain whether this is correct, referring to your graphs.

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