Since the total time of practice is 17 1/3 hours, then we can add the practice time of the three weeks to get the following equation:
[tex]17\frac{1}{3}=5\frac{1}{4}+5\frac{2}{3}+x[/tex]next,to find the number of hours of the third week, lets converte these mixed numbers into improper fractions:
[tex]\begin{gathered} 5\frac{1}{4}=\frac{21}{4} \\ 5\frac{2}{3}=\frac{17}{3} \\ 17\frac{1}{3}=\frac{52}{3} \end{gathered}[/tex]then, solving for x, we get:
[tex]\begin{gathered} \frac{52}{3}=\frac{21}{4}+\frac{17}{3}+x \\ \Rightarrow x=\frac{52}{3}-\frac{17}{3}-\frac{21}{4}=\frac{35}{3}-\frac{21}{4}=\frac{35\cdot4-21\cdot3}{12}=\frac{140-63}{12}=\frac{77}{12}=6\frac{5}{12} \end{gathered}[/tex]therefore, Rodrigo spent 6 5/12 hours practicing during the third week
