Ana can finish a certain job in 10 hours. Together, Ana and Nina can finish the same job in 3 hours. How many hours can Nina finish the job alone?

[tex]Ana: \dfrac{1}{10}\ \text{job per hour}\\\\Nina: \dfrac{1}{x}\ \text{job per hour}\\\\Together: \dfrac{1}{3}\ \text{job per hour}\\\\\\Ana + Nina = Together\\\dfrac{1}{10}\quad +\dfrac{1}{x}\quad =\quad \dfrac{1}{3}\\\\\\\dfrac{1}{10}(30x)+\dfrac{1}{x}(30x) =\dfrac{1}{3}(30x)\\\\\\\rightarrow\quad 3x+30=10x\\\\.\quad 3x+30=10x\\\underline{-3x\qquad \quad -3x\quad}\\.\qquad \quad 30=7x\\\\.\qquad \quad \dfrac{30}{7}=\dfrac{7x}{7}\\\\\\.\qquad \quad \dfrac{30}{7}=x[/tex]

[tex].\qquad \quad 4.5=x[/tex]

tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-15T05:25:47+02:00

Nina can finish the job alone in 4.3 hours. This is obtained by forming an equation and finding the solution for it.

What is the rational equation to work together?

The equation that represents the total work done together is given as [tex]\frac{1}{T}=\frac{1}{T_{A}}+\frac{1}{T_{B}}[/tex]. Where [tex]T_A[/tex] is the job done by A and [tex]T_B[/tex] is the job done by B.

Writing the equation:

Given that,

Ana can finish a certain job in 10 hours

⇒ The amount of work that Ana can finish in one hour = [tex]\frac{1}{10}[/tex]

Ana and Nina can finish the job in 3 hours

⇒ The amount of work that Ana and Nina can finish in one hour = [tex]\frac{1}{3}[/tex]

Considering that Nina can finish the job alone in x hours

⇒ The amount of work that Nina can finish in one hour = [tex]\frac{1}{x}[/tex]

So, the equation we can write as

[tex]\frac{1}{3}=\frac{1}{10}+\frac{1}{x}[/tex]

Solving for x:

The obtained equation is [tex]\frac{1}{3}=\frac{1}{10}+\frac{1}{x}[/tex]

On simplifying,

⇒ [tex]\frac{1}{x}=\frac{1}{3}-\frac{1}{10}[/tex]

⇒ [tex]\frac{1}{x}=\frac{7}{30}[/tex]

⇒ x = 4.28 ≅ 4.3

∴ Nina can finish the job alone in 4.3 hours.

Learn more about the work done problems here:

https://brainly.com/question/14031552

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