Problem 2. Ana, Maria, and Jovan received a text to translate from English to Macedonian. Ana and Maria, if they work together, need 30 hours to translate the text, Ana and Jovan need 42 hours, and Maria and Jovan need 35 hours. How much time (in hours and minutes) do Ana, Maria, and Jovan need to translate the text if they all work together?
Solution. Ana and Maria, if they work together, translate $\frac{1}{30}$ of the text in 1 hour. Ana and Ivan, if they work together, translate $\frac{1}{42}$ of the text in 1 hour. Maria and Ivan, if they work together, translate $\frac{1}{35}$ of the text in 1 hour. Therefore, if all three work together, in 1 hour they translate $\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{35}\right): 2=\frac{3}{70}$ of the text. If we denote the time needed to translate the entire text when all three work together as $T$, we get $\frac{3}{70} T=1$, or $T=\frac{70}{3}=23 \frac{1}{3} h$. Thus, it takes Ana, Maria, and Ivan 23 hours and 20 minutes to translate the text when they all work together.