Juan 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 How many hours last week.
Since Juan practiced the violin for 9 hours last week, and for every 3 hours he practices the violin, he practices the cello for 2.5 hours, this means that Juan practiced the cello for 2.5 hours/ 3 hours = 0.8333... hours for every hour he practiced the violin.
So Juan practiced the cello for 9 hours * 0.8333... = 7.5 hours last week.
Since Juan and Nina practiced the cello for the same amount of time, then Nina also practiced the cello for 7.5 hours last week.
Since for every 3 hours Nina spends practicing the viola, she practices the cello for 2 hours, this means Nina practiced the viola for 7.5 hours / (2 hours/3 hours) = <<7.5/(2/3)=11.25>>11.25 hours. Answer: \boxed{11.25}.