alone it takes kai 10 hours to complete a one-hour long presentation. it takes ted 8 hours to complete a one hour long presentation. using a rational equation, how long would it take them to complete a one hour long presentation if they worked together
Let's assume x is the time it would take them to complete a one-hour long presentation if they worked together.
Kai completes 1/10 of the presentation per hour (since he takes 10 hours to complete a one-hour presentation).
Ted completes 1/8 of the presentation per hour (since he takes 8 hours to complete a one-hour presentation).
Working together, Kai and Ted would complete 1/x of the presentation per hour.
According to the problem, Kai and Ted working together equals the sum of their individual work rates:
1/10 + 1/8 = 1/x
To find the common denominator, we multiply 10 and 8:
8/80 + 10/80 = 1/x
18/80 = 1/x
Now, we can cross-multiply to solve for x:
18x = 80
x = 80/18
x ≈ 4.44
Therefore, it would take them approximately 4.44 hours to complete a one-hour long presentation if they worked together.
To solve this problem using a rational equation, we can let x represent the time it takes for Kai and Ted to complete a one-hour presentation when they work together.
Since Kai takes 10 hours to complete a one-hour presentation on his own, his work rate can be expressed as 1/10 (1 presentation per 10 hours).
Similarly, since Ted takes 8 hours to complete a one-hour presentation on his own, his work rate can be expressed as 1/8 (1 presentation per 8 hours).
When they work together, their work rates add up, so we can create the following equation:
1/10 + 1/8 = 1/x
Now, we can solve this equation for x. To do that, we'll need to find a common denominator for 10 and 8, which is 40.
Multiplying each term by 40, we get:
4/40 + 5/40 = 1/x
Combining the fractions on the left side:
9/40 = 1/x
To remove the fraction, we can take the reciprocal of both sides:
x/1 = 40/9
Simplifying the expression on the right side:
x = 40/9
So, when Kai and Ted work together, it will take them approximately 4.44 hours (or 4 hours and 26 minutes) to complete a one-hour long presentation.
To determine how long it would take Kai and Ted to complete a one-hour long presentation if they worked together, we can use the concept of work rates.
First, let's find the work rates for Kai and Ted individually. The work rate is calculated by dividing the amount of work done by the time taken. In this case, the work rate is measured in presentations per hour.
Kai's work rate = 1 presentation / 10 hours = 1/10 presentations per hour
Ted's work rate = 1 presentation / 8 hours = 1/8 presentations per hour
Next, let's find the combined work rate when they work together. Since they are working on the same project, their work rates are additive.
Combined work rate = Kai's work rate + Ted's work rate
= 1/10 + 1/8 presentations per hour
= (4/40) + (5/40) presentations per hour
= 9/40 presentations per hour
Now, let's denote the time it takes for them to complete one presentation when they work together as 'x' hours.
Their combined work rate is (1/9) presentations per hour since they are completing one presentation in 'x' hours.
Setting up the rational equation:
(1 presentation) / (x hours) = 9/40 presentations per hour
Cross-multiplying:
40 * 1 = 9 * x
40 = 9x
Dividing both sides by 9:
40/9 = x
Hence, it would take Kai and Ted approximately 40/9 hours, or approximately 4.44 hours, to complete a one-hour long presentation if they worked together.