Two water tanks modelled by straight lines
Two water tanks modelled by straight lines
IP 1
7 marks
A full tank holds \(500\) litres. Water drains out at a constant rate. After \(4\) minutes the tank holds \(380\) litres; after \(10\) minutes it holds \(200\) litres. Let \(V\) litres be the volume after \(t\) minutes.
- Find the gradient of the graph of \(V\) against \(t\), and show that \(V=500-30t\).[3]
- Find the time at which the tank becomes empty.[1]
- A second tank, empty at first, starts filling at \(t=2\) at \(25\) litres per minute. Find the time at which the two tanks hold the same volume, and that volume.[2]
- State the range of values of \(t\) for which \(V=500-30t\) is a valid model for the first tank.[1]
Solution:
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Answer:(a) gradient \(-30\); \(c=500\), so \(V=500-30t\) (b) \(16\dfrac23\) minutes (c) \(t=10\), \(200\) litres (d) \(0\le t\le16\dfrac23\)
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