Let \( K \) be the rate at which Khalil works, and \( T \) be the rate at which Teddy works.
Khalil completes a one-hour presentation in 10 hours, so his work rate is: \[ K = \frac{1 \text{ presentation}}{10 \text{ hours}} = \frac{1}{10} \text{ presentations per hour} \]
Teddy completes a one-hour presentation in 8 hours, so his work rate is: \[ T = \frac{1 \text{ presentation}}{8 \text{ hours}} = \frac{1}{8} \text{ presentations per hour} \]
When they work together, their combined work rate is: \[ K + T = \frac{1}{10} + \frac{1}{8} \]
To add these fractions, we need a common denominator. The least common multiple of 10 and 8 is 40. Therefore, we can express each rate with a denominator of 40: \[ K = \frac{1}{10} = \frac{4}{40} \] \[ T = \frac{1}{8} = \frac{5}{40} \]
Now, we can add the two rates: \[ K + T = \frac{4}{40} + \frac{5}{40} = \frac{9}{40} \text{ presentations per hour} \]
Now, let \( x \) be the time in hours that it takes them to complete one presentation together. We know that their combined rate multiplied by time equals 1 presentation: \[ \left( \frac{9}{40} \right) x = 1 \]
Solving for \( x \): \[ x = \frac{1}{\frac{9}{40}} = \frac{40}{9} \text{ hours} \]
To get a decimal approximation: \[ x \approx 4.44 \text{ hours} \]
Therefore, together, Khalil and Teddy can complete a one-hour presentation in approximately \( \frac{40}{9} \) hours, or about 4.44 hours.