To find out how long it takes Khalil and Teddy to complete a one-hour presentation together, we can set up a rational equation based on their individual rates of work.
Step 1: Find their rates of work
- Khalil takes 10 hours for a one-hour presentation. His rate is \( \frac{1}{10} \) of the presentation per hour.
- Teddy takes 8 hours for a one-hour presentation. His rate is \( \frac{1}{8} \) of the presentation per hour.
Step 2: Find their combined rate
When working together, you add their rates:
\[
\text{Combined rate} = \frac{1}{10} + \frac{1}{8}
\]
Step 3: Find a common denominator
The least common multiple of 10 and 8 is 40. We rewrite their rates:
\[
\frac{1}{10} = \frac{4}{40} \quad \text{and} \quad \frac{1}{8} = \frac{5}{40}
\]
Now add them:
\[
\frac{4}{40} + \frac{5}{40} = \frac{9}{40}
\]
So together, they complete \( \frac{9}{40} \) of the presentation in one hour.
Step 4: Find the time to complete one presentation
To find the time \( t \) it takes to complete one full presentation when working together, use the equation:
\[
\frac{9}{40}t = 1
\]
Now, solve for \( t \):
\[
t = \frac{1}{\frac{9}{40}} = \frac{40}{9}
\]
Step 5: Calculate \( t \)
Now, \( \frac{40}{9} \approx 4.44 \) hours, or about 4 hours and 27 minutes.
So, working together, Khalil and Teddy can complete a one-hour presentation in about 4 hours and 27 minutes.