It takes 3 tractors to seed 400 hectares in 5 days.
Tractors | Hectares | Days |
3 | 400 | 5 |
2 | 350 | \(x \) |
As the number of tractors has decreased, we will require more time. Therefore, from the numbers in the first column, we create the fraction that is greater than 1 (i.e. \( \frac{3}{2} \))
As the number of hectares has decreased, we will require less time. Therefore, from the numbers in the second column, we create the fraction that is less than 1 (i.e. \( \frac{350}{400} \))
\begin{align} So \quad x & =\frac{3}{2}\ \times\ \frac{350}{400}\ \times\ 5 \\ \\ & = \frac{3}{2}\ \times\ \frac{7}{8}\ \times\ 5 \\ \\ & = \frac{105}{16} \\ \\ & = 6 \frac{9}{16}\ days \end{align}Tractors | Hectares | Days |
3 | 400 | 5 |
\(x \) | 450 | 1 |
As the number of hectares has increased, we will require more tractors. Therefore, from the numbers in the second column, we create the fraction that is greater than 1 (i.e. \( \frac{450}{400} \))
As the number of days has decreased, we will require more tractors. Therefore, from the numbers in the third column, we create the fraction that is greater than 1 (i.e. \( \frac{5}{1} \))
\begin{align} So \quad x & =\frac{450}{400}\ \times\ \frac{5}{1}\ \times\ 3 \\ \\ & = \frac{9}{8}\ \times\ \frac{5}{1}\ \times\ 3 \\ \\ & = \frac{135}{8} \\ \\ & = 16.875 \quad tractors \\ \end{align}But as a part-tractor is nonsense, we need 17 tractors