To determine how long it would take Khalil and Teddy to complete a one-hour presentation when they work together, we can use the concept of their work rates.
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Find the work rates of Khalil and Teddy:
- Khalil takes 10 hours to complete a one-hour presentation, so his work rate is \( \frac{1 \text{ hour}}{10 \text{ hours}} = \frac{1}{10} \) of a presentation per hour.
- Teddy takes 8 hours to complete a one-hour presentation, so his work rate is \( \frac{1 \text{ hour}}{8 \text{ hours}} = \frac{1}{8} \) of a presentation per hour.
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Combine their work rates: When they work together, their combined work rate is the sum of their individual work rates: \[ \text{Combined work rate} = \frac{1}{10} + \frac{1}{8} \]
To add these fractions, we need a common denominator. The least common multiple of 10 and 8 is 40.
- Convert \( \frac{1}{10} \) to have a denominator of 40: \[ \frac{1}{10} = \frac{4}{40} \]
- Convert \( \frac{1}{8} \) to have a denominator of 40: \[ \frac{1}{8} = \frac{5}{40} \]
Now, add the two fractions: \[ \text{Combined work rate} = \frac{4}{40} + \frac{5}{40} = \frac{9}{40} \]
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Calculate the time to complete the presentation together: Let \( t \) be the time (in hours) it takes for them to complete the one-hour presentation together. The equation will be: \[ \left(\frac{9}{40}\right) t = 1 \quad \text{(since they need to complete 1 full presentation)} \]
To find \( t \), rearrange the equation: \[ t = \frac{1}{\frac{9}{40}} = \frac{40}{9} \]
Hence, \( t \approx 4.44 \), which can also be expressed as: \[ t \approx 4 \text{ hours and } 26.67 \text{ minutes} \]
Therefore, Khalil and Teddy can complete a one-hour presentation together in approximately 4 hours and 27 minutes.
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