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, which of the following correctly calculates how long it would take them to complete a one-hour long presentation if they worked together?
To solve the problem using a rational equation, we can assign variables to represent the time it takes each person to complete a one-hour presentation. Let's assign "x" to Khalil's time and "y" to Teddy's time.
Based on the given information, we know that Khalil takes 10 hours to complete a one-hour presentation, so his rate of work would be 1/10 (1 hour completed / 10 hours worked). Similarly, Teddy takes 8 hours to complete a one-hour presentation, so his rate of work would be 1/8 (1 hour completed / 8 hours worked).
When they work together, their rates of work will add up, so we can set up the following equation:
1/x + 1/y = 1/t
Where "t" represents the time it would take them together to complete a one-hour presentation.
Substituting the rates of work, we have:
1/10 + 1/8 = 1/t
To simplify this equation, we need to find a common denominator, which is 40 in this case:
4/40 + 5/40 = 1/t
Combining the fractions:
9/40 = 1/t
To solve for "t", we can cross-multiply:
9t = 40
Dividing both sides by 9:
t = 40/9
Therefore, when Khalil and Teddy work together, it would take them approximately 4.44 hours to complete a one-hour long presentation.
To determine how long it would take Khalil and Teddy to complete a one-hour long presentation when working together, we can use the concept of "work rates."
Let's assume it takes Khalil 'k' hours to complete a one-hour long presentation, and it takes Teddy 't' hours to complete the same presentation.
We can express their work rates as:
Khalil's work rate: 1 presentation / 10 hours = 1/10 presentations per hour
Teddy's work rate: 1 presentation / 8 hours = 1/8 presentations per hour
When working together, their work rates should be added:
Khalil and Teddy's combined work rate: 1/10 presentations per hour + 1/8 presentations per hour
To add these rates together, we need a common denominator. The least common denominator (LCD) between 10 and 8 is 40.
Multiplying the first rate by 4/4 and the second rate by 5/5 (which is equivalent to multiplying by 1) and simplifying, we get:
Khalil and Teddy's combined work rate: (4/40) + (5/40) = 9/40 presentations per hour
Thus, Khalil and Teddy working together can complete 9/40 of a presentation in one hour.
Now, we can set up a rational equation to find the time it would take them to complete a one-hour long presentation when working together, represented by 'x':
(9/40) presentations / 1 hour = 1 presentation / x hours
Cross-multiplying, we have:
9x = 40
To solve for 'x,' divide both sides of the equation by 9:
x = 40/9
Therefore, it would take Khalil and Teddy approximately 40/9 hours (or approximately 4.44 hours) to complete a one-hour long presentation if they worked together.
To calculate how long it would take Khalil and Teddy to complete a one-hour long presentation if they worked together, we can use a rational equation based on their individual rates of work.
Let's denote the time it takes Khalil to complete the presentation as K, and the time it takes Teddy to complete the presentation as T.
According to the problem, Khalil takes 10 hours to complete a one-hour long presentation. So we can write the equation as:
K = 10
Similarly, Teddy takes 8 hours to complete a one-hour long presentation, so we can write the equation as:
T = 8
Now, when they work together, their rates of work are additive. This means that their combined rate of work is equal to the sum of their individual rates. The rate of work is inversely proportional to the time taken, so we can represent it as 1/t, where t is the time taken.
So, the equation for their combined rate of work can be written as:
1/K + 1/T = 1/t
Substituting the values of K and T, we get:
1/10 + 1/8 = 1/t
To simplify the equation, we can find the least common multiple (LCM) of 10 and 8, which is 40. Multiplying all terms in the equation by 40, we have:
4 + 5 = 40/t
9 = 40/t
Now, we can cross multiply:
9t = 40
Dividing both sides by 9, we get:
t = 40/9
Therefore, it would take Khalil and Teddy working together approximately 4.44 hours (or 4 hours and 26 minutes) to complete a one-hour long presentation.