Two 2

Two different harvesters harvested potatoes with an area of 6.6 ha in one shift when they were operating simultaneously. The area of land from which the less powerful harvester was able to harvest potatoes in six shifts, the more powerful harvester in 5 shifts. Determine the area of land from which each of the harvesters was able to harvest potatoes in 1 shift.

Final Answer:

a =  3 ha
b =  3.6 ha

Step-by-step explanation:

$$\begin{gathered} a+b=6.6 \\ 6a=5b \\ 6\cdot a=5\cdot b \\ 6a-5b=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ 1.83b=6.6 \\ b=\frac{6.6}{1.83333333}=3.6 \\ a=\frac{0+5b}{6}=\frac{0+5\cdot 3.6}{6}=3=3\text{ha} \\ a=3 \\ b=\frac{18}{5}=3.6 \end{gathered}$$

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