Mathematics, 15.04.2020 03:24 JamierW2005

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?

Answers: 1

Show answers

Answers

Answer from: Echo009

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:

$\rm t \;\alpha \;\dfrac{L}{N}$

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:

$\rm t = k\times \dfrac{L}{N}$ ---- (1)

where k is the proportionality constant.

Now, substitute the known terms in order to determine the value of K.

$\rm 14=K\dfrac{12}{150}$

Cross multiply in the above expression.

$\rm 150\times 14 = K \times 12$

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).

$\rm t = \dfrac{175\times 15}{125}$

Simplify the above expression in order to get the value of 't'.

$\rm t = \dfrac{2625}{125}$

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:

link

Answer from: Geo777

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

Answer from: Quest

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6

Answer from: Quest

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.

Another question on Mathematics

Mathematics, 21.06.2019 14:00

Design a number line containing five (5) points2.benin, one of the smallest countries in africa, has a total area of 43,475 square miles. the population of the country was recently estimated at 10,160,555. about 3,657,790 people live in rural areas. the country has only about 870 miles of surfaced roads. a. round off the total population to the nearest hundred thousand people. b. round off benin’s area in square miles to the nearest thousand. c. round off the number of miles of surfaced roads to the nearest ten. d. round off the number of people who live in rural areas to the nearest million.

Answers: 3

Answer

Mathematics, 21.06.2019 17:00

How many of the 250 grandparents in the population would you expect to prefer online shopping with merchant a? merchant a: 4 merchant b: 6 merchant c: 2 merchant d: 3 other: 5 none: 5 answer choices: a.about 4 b.about 8 c.about 40 d.about 21

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Hi, can anyone show me how to do this problem? 100 points for this. in advance

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3

Answers: 1

Answer

You know the right answer?

Suppose that the amount of time it takes to build a highway varies directly with the length of the h...