Question

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?
A. 30 men
B. 270 men
C. 35 men
D. 28 men

Answer 1

ANSWER

C. 35 men

EXPLANATION

Let m represent the number of men needed and d represent the number of days.

From the question,the number of men needed varies inversely to the time needed to complete the project.

We can write the inverse variation equation.

$m = \frac{k}{d}$

where k is the constant of variation.

When m=28, d =90.

We substitute these values into the variation equation to determine the value of k.

$28 = \frac{k}{90}$

$k = 90 \times 28$

$k = 252$

Now the equation becomes:

$m= \frac{2520}{d}$

When d=72,

$m = \frac{2520}{72}$

$m = 35$

Therefore he needs to have 35 men working.