Answer:
It will take 5 days for 12 men to do the same work.
Step-by-step explanation:
The number of men varies inversely as the number of days.
Let m be the number of men, and d be the number of days.
Mathematical Equation:
[tex]\LARGE\text{$m=\frac{k}{d}$}[/tex]
For the constant of variation (k):
Given: [tex]m=3[/tex], [tex]d=20[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]m=\frac{k}{d}[/tex]
Solution:
[tex]m=\frac{k}{d}\\3=\frac{k}{20}\\k=(3)(20)\\\boldsymbol{k=60}[/tex]
For the number of days (d) if there are 12 men (m):
Given: [tex]k=60[/tex], [tex]m=12[/tex]
Find: [tex]d=?[/tex]
Formula: [tex]m=\frac{k}{d}[/tex]
Solution:
[tex]m=\frac{k}{d}\\12=\frac{60}{d}\\12d=60\\\frac{12d}{12}=\frac{60}{12}\\\boxed{\boldsymbol{d=5}}[/tex]
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