Respuesta :
Answer:
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
The time required by 125 workers to build 15 miles of highway is 21 weeks and this can be determined by forming an mathematical expression with the help of the given data.
Given :
- 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 that it takes 150 workers 14 weeks to build 12 miles of highway.
According to the given data 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 that is:
[tex]\rm t \;\alpha \;\dfrac{L}{N}[/tex]
where t is the time taken to build the highway, L is the length of the highway and N is the number of workers.
So, the mathematical expression of the above relationship is:
[tex]\rm t = k\times \dfrac{L}{N}[/tex] ---- (1)
where k is the proportionality constant.
Now, substitute the known terms in order to determine the value of K.
[tex]\rm 14=K\dfrac{12}{150}[/tex]
Cross multiply in the above expression.
[tex]\rm 150\times 14 = K \times 12[/tex]
2100 = 12K
175 = K
Now, substitute the values of K that is 175, N that is 125, and L that is 15 in the equation (1).
[tex]\rm t = \dfrac{175\times 15}{125}[/tex]
Simplify the above expression in order to get the value of 't'.
[tex]\rm t = \dfrac{2625}{125}[/tex]
t = 21 weeks
So, the time required by 125 workers to build 15 miles of highway is 21 weeks.
For more information, refer to the link given below:
https://brainly.com/question/2263981
