alone it takes Khalil 10 hours to complete a one-hour long presentation. it takes Teddy 8 hours to complete a one hour long presentation using a rational equation calculate how long it would take them to complete a one hour presentation if they work together

you may solve algebraically or graphically

explain simpler without commas

1 answer

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.