Answer:
8 days
Step-by-step explanation:
Direct Variation takes the form \(A=kB\) , and
Inverse Variation takes the form \(A=k(\frac{1}{B})\)
Where
- \(A\) and \(B\) are the 2 variables associated, and
- \(k\) is the proportionality constant
From the statement of the problem given, and taking time as \(t\) and length as \(l\) and number of men working as \(n\)
We can write:
\(t=\frac{kl}{n}\)
Using the values given in the problem ( \(t=2\) , \(n=8\) , and \(l=100\) ), we can solve for k:
\(2=\frac{(k)(100)}{8}\\16=k*100\\k=\frac{16}{100}=0.16\)
Now, we want to know time given \(n=3\) and \(l=150\) and \(k=0.16\)
\(t=\frac{(0.16)(150)}{3}\\3t=(0.16)(150)\\3t=24\\t=\frac{24}{3}\\t=8\)
So, it will take 8 days.
