Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Jeff and Kirk can build a​ 75-ft retaining wall together in 4 hours. Because Jeff has more​ experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk​ (to the nearest​ minute) to build the wall by​ himself?

Sagot :

sqdancefan

Answer:

  8 hours 32 minutes

Step-by-step explanation:

Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.

__

setup

Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

  1/k +1/(k -1) = 1/4

__

solution

Multiplying by 4k(k-1), we have ...

  4(k-1) +4k = k(k -1)

  k² -9k = -4 . . . . . . . . subtract 8k and simplify

  k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

  k -4.5 = √16.25 . . . . . . . . . take the square root

  k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

  0.531129 × 60 min ≈ 31.9 min ≈ 32 min

It would take Kirk about 8 hours 32 minutes to build the wall by himself.

_____

Additional comment

For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.

ashishdwivedilVT

It will take Kirk about 8 hours 32 minutes to build the wall by himself.

What is Quadratic Polynomial?

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

 1/k +1/(k -1) = 1/4

Multiplying by 4k(k-1), we have ...

 4(k-1) +4k = k(k -1)

 k² -9k = -4 . . . . . . . . subtract 8k and simplify

 k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

 k -4.5 = √16.25 . . . . . . . . . take the square root

 k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

 0.531129 × 60 min ≈ 31.9 min ≈ 32 min

Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.

Learn more about Quadratic Polynomial from:

https://brainly.com/question/2350120

#SPJ1

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.