Alone, it takes Kahil 10 hours to complete a one hour long presentation. It takes Teddy eight hours to complete a one hour long presentation using a rational equation which of the following correctly calculates how long it would take them to complete a one hour long presentation if they work together
Let's denote the time it takes them to complete a one-hour long presentation when they work together as "t". We can solve this problem using the concept of work.
Since Kahil takes 10 hours to complete a one-hour long presentation, his work rate is 1/10 presentations per hour.
Similarly, since Teddy takes 8 hours to complete a one-hour long presentation, his work rate is 1/8 presentations per hour.
When they work together, their work rates are additive. Thus, the equation representing their combined work rate is:
1/10 + 1/8 = 1/t
To solve for "t", we can multiply both sides of the equation by the least common denominator, which is 40 in this case:
8 + 10 = 40/t
18 = 40/t
Now we can solve for "t" by cross-multiplying:
18t = 40
t = 40/18
t = 20/9
Therefore, it would take them approximately 2.22 (repeating) hours to complete a one-hour long presentation if they work together.
To calculate how long it would take Kahil and Teddy to complete a one hour long presentation when they work together, we can use the concept of work rates.
Kahil takes 10 hours to complete a one hour long presentation. Therefore, his work rate is 1/10 presentations per hour.
Teddy takes 8 hours to complete a one hour long presentation using a rational equation. Hence, his work rate is 1/8 presentations per hour.
When they work together, their work rates will add up. Therefore, the combined work rate of Kahil and Teddy is:
1/10 + 1/8 = 4/40 + 5/40 = 9/40 presentations per hour.
To determine the time it would take them to complete a one hour long presentation together, we can find the reciprocal of their combined work rate:
1 / (9/40) = 40/9.
Therefore, it would take Kahil and Teddy approximately 40/9 hours to complete a one hour long presentation if they work together.
To calculate the time it would take Kahil and Teddy to complete a one-hour long presentation together, we'll use the concept of rates.
Let's assume Kahil's rate of completing a one-hour presentation is "1 presentation per 10 hours." Similarly, Teddy's rate is "1 presentation per 8 hours."
To find their combined rate, we need to add their individual rates. Thus, their combined rate becomes "1 presentation per 10 hours + 1 presentation per 8 hours."
To add these rates, we need to find a common denominator. In this case, the least common multiple of 10 and 8 is 40.
Multiplying Kahil's rate by 4/4 (to get a denominator of 40) gives us "4 presentations per 40 hours."
Multiplying Teddy's rate by 5/5 (to get a denominator of 40) gives us "5 presentations per 40 hours."
Now that their rates have a common denominator, we can add them together:
4 presentations per 40 hours + 5 presentations per 40 hours = 9 presentations per 40 hours.
Therefore, working together, Kahil and Teddy would complete 9 presentations in 40 hours.
Since we need to find the time it takes to complete one presentation, we can set up a proportion:
9 presentations per 40 hours = 1 presentation per x hours.
By cross-multiplying, we get:
9x = 40.
Dividing both sides by 9, we find:
x = 40 / 9.
So, it would take Kahil and Teddy approximately 4 and 4/9 hours to complete a one-hour long presentation if they work together.
The correct option for the rational equation representing this calculation is:
(10 * 8) / (10 + 8), which simplifies to 80 / 18 or 4 and 4/9 hours.