jeff and kirk can build a 75-ft retaining wall together in 9 hours. because jeff has more experience, he could build the wall by himself 2 hours quicker than kirk. how long would it take kirk (to the nearest minute) to build the wall by himself?

it will take kirk approximately hours min to build the wall himself.
(round to the nearest minute as needed.)

Question

jeff and kirk can build a 75-ft retaining wall together in 9 hours. because jeff has more experience, he could build the wall by himself 2 hours quicker than kirk. how long would it take kirk (to the nearest minute) to build the wall by himself?

it will take kirk approximately hours min to build the wall himself.
(round to the nearest minute as needed.)

it will take kirk approximately   hours   min to build the wall himself.
(round to the nearest minute as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Work Rate Problems", "Rational Equations", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Work Rate Problems", "Rational Equations", "Quadratic Formula Application" ] } ## Set up the work rate equation $$ \begin{aligned} &\text{Let } x = \text{time for Kirk to build the wall alone (in hours)}\ &\text{Jeff's time alone } = x - 2 \text{ hours}\ &\frac{1}{x} + \frac{1}{x-2} = \frac{1}{9} \end{aligned} $$ ## Solve the rational equation for x $$ \begin{aligned} &9(x-2) + 9x = x(x-2)\ &18x - 18 = x^2 - 2x\ &x^2 - 20x + 18 = 0\ &x = \frac{20 \pm \sqrt{(-20)^2 - 4(1)(18)}}{2}\ &x = \frac{20 \pm \sqrt{328}}{2} = 10 \pm \sqrt{82}\ &x \approx 10 + 9.055385 = 19.055385 \text{ hours} \quad (x > 2) \end{aligned} $$ ## Convert decimal hours to hours and minutes $$ \begin{aligned} &\text{Hours} = 19\ &\text{Minutes} = 0.055385 \times 60 \approx 3.323 \approx 3 \text{ minutes} \end{aligned} $$ It will take Kirk approximately 19 hours 3 min to build the wall himself. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Work Rate Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the work rate equation

Solve the rational equation for x

Convert decimal hours to hours and minutes

Answer: