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Algebra, STD2 EQ-Bank 11

The amount of water (\(W\)) in litres used by a garden irrigation system varies directly with the time (\(t\)) in minutes that the system operates.

This relationship is modelled by the formula \(W=kt\), where \(k\) is a constant.

The irrigation system uses 96 litres of water when it operates for 24 minutes.

  1. Show that the value of \(k\) is 4.   (1 mark)
  2. The water tank for the irrigation system contains 650 litres of water. Calculate how many minutes the irrigation system can operate before the tank is empty.   (2 marks)
Show Answers Only

a.    \(W=kt\)

\(\text{When } W = 96 \text{ and } t = 24:\)

\(96\) \(=k \times 24\)
\(k\) \(=\dfrac{96}{24}\)
\(k\) \(=4\ \text{(as required)}\)

b.     \(162.5\ \text{minutes}\)

Show Worked Solution

a.    \(W=kt\)

\(\text{When } W = 96 \text{ and } t = 24:\)

\(96\) \(=k \times 24\)
\(k\) \(=\dfrac{96}{24}\)
\(k\) \(=4\ \text{(as required)}\)

  
b.    \(W = 4t\)

\(\text{When } W = 650:\)

\(650\) \(=4\times t\)
\(t\) \( =\dfrac{650}{4}\)
  \(=162.5\ \text{minutes}\)

    
\(\therefore\ \text{The irrigation system can operate for } 162.5 \text{ minutes.}\)