To determine how long it would take Khalil and Teddy to complete a one-hour presentation if they worked together, we can use the concept of rates.
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Calculate the rates of each person:
- Khalil's rate: He completes 1 hour of presentation in 10 hours, so his rate is \( \frac{1}{10} \) presentations per hour.
- Teddy's rate: He completes 1 hour of presentation in 8 hours, so his rate is \( \frac{1}{8} \) presentations per hour.
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Combine their rates:
- Together, their combined rate is: \[ \frac{1}{10} + \frac{1}{8} \]
To add these fractions, we first find a common denominator, which is 40.
- Convert the fractions: \[ \frac{1}{10} = \frac{4}{40} \] \[ \frac{1}{8} = \frac{5}{40} \]
So, we have: \[ \frac{4}{40} + \frac{5}{40} = \frac{9}{40} \]
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Find the time to complete 1 presentation together:
- If they can complete \( \frac{9}{40} \) of a presentation in 1 hour, then to complete 1 full presentation, we set up the equation: \[ \text{Time} = \frac{1 \text{ presentation}}{\frac{9}{40} \text{ presentations/hour}} = \frac{40}{9} \text{ hours} \]
Dividing \( 40 \) by \( 9 \) gives: \[ \frac{40}{9} \approx 4.44 \text{ hours} \]
Thus, the answer is 4.44 hours.