Jeff and Kirk can build a 75-ft retaining wall together in 4 hours. Because Jeff has more experience, he could build the wall

Question

Alex_Xolod [135]

1 year ago

10

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?

Mathematics

2 answers:

oee [108] · Answer 1 · 2023-02-12T10:52:34+03:00

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

<h3>What is Quadratic Polynomial?</h3>

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:

brainly.com/question/2350120

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LiRa [457] · Answer 2 · 2023-02-12T12:34:50+03:00

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.

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<h3>setup</h3>

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

__

<h3>solution</h3>

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.

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<em>Additional comment</em>

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.