Susan 5

Susan has a water tank in his back garden that can hold up to 750L in water. At the start of a rainy day (at 0:00) there is 165L in the tank, and after a heavy day’s rain (at 24:00) there is 201 L in the tank.

Assuming that the rain fell consistently during the 24-hour period, set up a linear equation to represent the amount of rain in the tank at any point during the day to determine the time of day at which the amount of water in the tank reached 192 L.

Result

t₃ = 18:00 h

Step-by-step explanation:

$$\begin{gathered} t_0=0 \\ {V}_1=165\text{l} \\ {t}_2=24.00 \\ {V}_2=201\text{l} \\ {V}_3=192\text{l} \\ V(t)=a\cdot t+b \\ V(0)=a\cdot 0+b \\ b=V_1=165\text{l} \\ {V}_2=a\cdot t_2+b \\ 201=a\cdot 24+165 \\ 24a=36 \\ a=\frac{36}{24}=1.5 \\ a=\frac{3}{2}=1.5 \\ {V}_3=a\cdot t_3+b \\ {t}_3=\frac{V_3-b}{a}=\frac{192-165}{1.5}=18=18:00\text{h} \end{gathered}$$

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