Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 150 workers 14 weeks to build 12 miles of highway. How long will it take 125 workers to build 15 miles of highway?

21 weeks

Step-by-step explanation:

In this question, we are to use proportionality to find the solution to the question.

We were made to know that the time taken to build the highway is varied directly with the length and inversely with the number of workers.

Let us make a mathematical representation for this.

Let the time be t, number of workers be w and length be l

t is directly proportional to l and inversely proportional to w

Mathematically;

t = kl/w

Where k is the constant of proportionality.

Let's find the value of k

150 workers built 12 miles of highway in 14 weeks; plug these in the equation to get k

14 = k * 12/150

k = 150 * 14/12 = 175

Now we want to get t given w and l

from;

t = kl/w

We can get t; where l = 15 and w = 125

t = 175 * 15/125

t = 21 weeks

21 weeks

Step-by-step explanation:

Let's assume that the amount of time it takes to build the highway to be "t" and the length to be "l" and the number of workers to be "w".

And its says that "t" varies directly with "l" and inversely with "w".

That is mathematically represented as

T ∞ l/w

T = kl/w

When t = 14, l = 12 and w = 150

K = wt/l

= 150 * 14 : 12

K = 175.

Now we are told to find the value of "t" when w = 125 and l = 15

T = kl/w

T = 175 * 15 : 125

T = 21 weeks