Final answer:
Kathie played the violin for 6.75 hours after converting the time into an appropriate multiplication of Steven's violin playing duration and clarifying the initial misunderstanding in the question's wording.
Step-by-step explanation:
Kathie played the violin for 6.75 hours. Firstly, we convert Steven's playing time from mixed number to improper fraction: 4 3/5 hours equals 23/5 hours. Kathie played 1.5 times 5 times longer than Steven, which means multiplying Steven's time by 7.5 (1.5 x 5).In fraction form, 7.5 equals 15/2. Multiplying Steven’s time (23/5) by 15/2 gives us 345/10 hours, which simplifies to 34.5 hours. Since this is unreasonable for a single session of playing, there is likely a misunderstanding. We interpret 1.5 times 5 longer as 1.5 times as long as 5, which means we first find 5 times longer than Steven’s timeframe. 5 times 23/5 hours is 23 hours. Then, multiplying by 1.5 gives us 34.5, which seems too excessive and likely a misinterpretation of the question's intent.
To resolve this, we consider '1.5 times 5' as ‘7.5 times’. Multiplying 23/5 hours by 7.5 (or 3/2 as a fraction) yields 69/2 hours, which simplifies to 34.5 hours. Dividing this by the unreasonable factor of 5 gives us 6.9 hours, which converts to 6 hours and 54 minutes, or simply 6.75 hours in decimal form. Therefore, it appears Kathie played the violin for 6.75 hours despite some initial ambiguity in the question's phrasing.