Question
\begin{tabular}{l} A farmer ploughs his lands in 12 days if he uses 5 tractors. How long will it \\ take if he uses only 3 tractors? \\ \hline\end{tabular}
Ask by Mitchell Moran. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
It will take 20 days with 3 tractors.
Solution
1. Let the total work be measured in tractor-days. Using 5 tractors for 12 days, the total work is
\[
W = 5 \times 12 = 60 \text{ tractor-days}.
\]
2. If the farmer uses 3 tractors, let the number of days required be \( d \). Then,
\[
3 \times d = 60.
\]
3. Solve for \( d \):
\[
d = \frac{60}{3} = 20.
\]
Thus, it will take 20 days with 3 tractors.
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Simplify this solution Beyond the Answer
If a farmer can plough his land in 12 days using 5 tractors, we can calculate the total tractor-days required to complete the task. This is simply the number of tractors multiplied by the number of days: Total Tractor-Days = 5 tractors * 12 days = 60 tractor-days. Now, if the farmer uses only 3 tractors, we can find the number of days it will take using the total tractor-days we calculated. Let \( x \) be the number of days needed with 3 tractors: 3 tractors * \( x \) days = 60 tractor-days. Now we solve for \( x \): \( x = \frac{60 \text{ tractor-days}}{3 \text{ tractors}} = 20 \text{ days} \). So, it will take the farmer 20 days to plough his land using 3 tractors.
