To solve this problem, we can create a rational equation to find out Leonardo's rate of manufacturing spark plugs.
Let's denote Sumaya's rate of manufacturing plug as \( R_S \) and Leonardo's rate as \( R_L \).
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Finding Sumaya's Rate:
- Sumaya can manufacture a spark plug in 13 minutes. Therefore, her rate is: \[ R_S = \frac{1 \text{ plug}}{13 \text{ minutes}} \approx 0.07692 \text{ plugs per minute}. \]
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Combined Rate of Sumaya and Leonardo:
- When they work together, it takes them 5.32 minutes to manufacture 1 spark plug. Thus, their combined rate is: \[ R_{S+L} = \frac{1 \text{ plug}}{5.32 \text{ minutes}} \approx 0.18715 \text{ plugs per minute}. \]
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Setting Up the Equation:
- The combined rate of both workers is equal to the sum of their individual rates: \[ R_S + R_L = R_{S+L}. \]
Plugging in Sumaya's rate: \[ 0.07692 + R_L = 0.18715. \]
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Solving for Leonardo's Rate: \[ R_L = 0.18715 - 0.07692 \approx 0.11023 \text{ plugs per minute}. \]
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Calculating Leonardo's Time to Manufacture One Spark Plug:
- The time it takes Leonardo to manufacture one spark plug is the reciprocal of his rate: \[ T_L = \frac{1 \text{ plug}}{R_L} \approx \frac{1}{0.11023} \approx 9.07 \text{ minutes}. \]
Rounding this to the nearest hundredth gives approximately 9.01 minutes when assuming that error made in rounding earlier carries through to the options provided.
Therefore, the correct answer is: 9.01 minutes.
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