A certain project can be completed by 28 men in 90 days. The numbers of men needed varies inversely to the time needed to complete the project. If the contractor wants to complete the project in 72 days, how many men does he have to have working?
30 men
270 men
35 men
28 men
In this situation, we can use the formula for inverse variation, which is:
\(M_1 \times D_1 = M_2 \times D_2\)
where:
- \(M_1\) = Number of men for first scenario
- \(D_1\) = Time for first scenario
- \(M_2\) = Number of men for second scenario
- \(D_2\) = Time for second scenario
Given data:
\(M_1 = 28\), \(D_1 = 90\), \(D_2 = 72\)
Let's find \(M_2\):
\(28 \times 90 = M_2 \times 72\)
\(M_2 = (28 \times 90) / 72\)
\(M_2 = 35\)
Therefore, to complete the project in 72 days, the contractor would need 35 men. So the answer is 35 men.