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Clare follows the same workout cycle each time she goes to the gym. First, she runs for 13\frac{1}{3} of an hour. Then, she lifts weights for 16\frac{1}{6} of an hour. If Clare has 1121\frac{1}{2} hours to spend at the gym, how many times can she go through her workout cycle?\newlineWrite your answer as a whole number, fraction, or mixed number. Simplify any fractions. \newline____ times

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Q. Clare follows the same workout cycle each time she goes to the gym. First, she runs for 13\frac{1}{3} of an hour. Then, she lifts weights for 16\frac{1}{6} of an hour. If Clare has 1121\frac{1}{2} hours to spend at the gym, how many times can she go through her workout cycle?\newlineWrite your answer as a whole number, fraction, or mixed number. Simplify any fractions. \newline____ times
  1. Calculate total workout time: Calculate the total time Clare spends per workout cycle by adding the time she runs and the time she lifts weights.\newline13\frac{1}{3} hour (running) + 16\frac{1}{6} hour (lifting) = (26+16)\left(\frac{2}{6} + \frac{1}{6}\right) hour = 36\frac{3}{6} hour = 12\frac{1}{2} hour.
  2. Determine workout cycles: Determine how many full workout cycles Clare can complete in her total gym time of 1121 \frac{1}{2} hours.\newline1121 \frac{1}{2} hours = 32\frac{3}{2} hours.\newlineNumber of cycles = Total gym time / Time per cycle = (32)/(12)=32×21=3\left(\frac{3}{2}\right) / \left(\frac{1}{2}\right) = \frac{3}{2} \times \frac{2}{1} = 3.

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