uan and Nina are in the Junior High Orchestra. As part of the orchestra they each have to learn two instruments. Juan is learning to play the violin and the cello. For every 3 hours that Juan spends practicing the violin he practices the cello for 2.5 hours. Nina is learning to play the viola and cello. For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours.
If Juan practiced the violin for 9 hours last week and Juan and Nina practiced the cello for the same amount of time, then Nina practiced the viola for
hours last week.
For every 3 hours Juan practices the violin, he practices the cello for 2.5 hours. So for every 3 hours of violin practice, Juan practices a total of 3 + 2.5 = 5.5 hours.
If Juan practiced the violin for 9 hours last week, he would have practiced the cello for 9 / 3 * 2.5 = 7.5 hours last week.
Since Juan and Nina practiced the cello for the same amount of time, Nina also practiced the cello for 7.5 hours last week.
For every 3 hours Nina practices the viola, she practices the cello for 2 hours. So for every 3 hours of viola practice, Nina practices a total of 3 + 2 = 5 hours.
Since Nina practiced the cello for 7.5 hours last week, she would have practiced the viola for 7.5 / 5 * 3 = 4.5 hours last week.
Therefore, Nina practiced the viola for 4.5 hours last week.