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Tamiku [17]
2 years ago
6

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 fin

ish the job alone?
Mathematics
1 answer:
Over [174]2 years ago
5 0

Answer:   4.5 hours

<u>Step-by-step explanation:</u>

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

.\qquad \quad 4.5=x

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