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? (1 point)
18 hours
4.44 hours
0.225 hours
9 hours
To find how long it would take them to complete a one-hour long presentation together, we can use the formula:
1 / (time taken by Khalil) + 1 / (time taken by Teddy) = 1 / (total time taken together)
Let's substitute the given values into the formula:
1 / 10 + 1 / 8 = 1 / (total time taken together)
Simplifying the left side:
0.1 + 0.125 = 1 / (total time taken together)
0.225 = 1 / (total time taken together)
Now we can isolate the total time taken together by taking the reciprocal of both sides:
(total time taken together) = 1 / 0.225
(total time taken together) = 4.44 hours
Therefore, the correct answer is:
4.44 hours.
To calculate how long it would take Khalil and Teddy to complete a one-hour presentation together using a rational equation, we can use the equation:
1 / x = 1 / 10 + 1 / 8
Where x represents the time it would take them to complete the presentation together.
Combining the fractions on the right side of the equation, we have:
1 / x = (8 + 10) / (10 * 8) = 18 / 80
To isolate x, we can take the reciprocal of both sides of the equation:
x = 80 / 18
Dividing 80 by 18, we get:
x ≈ 4.44 hours
Therefore, the correct answer is 4.44 hours.
To determine how long it would take Khalil and Teddy to complete a one-hour presentation if they worked together, we can use the concept of work rates.
We know that Khalil takes 10 hours to complete a one-hour presentation, so his work rate can be calculated as 1/10 (since he completes 1 presentation in 10 hours).
Similarly, Teddy takes 8 hours to complete a one-hour presentation, so his work rate is 1/8 (1 presentation in 8 hours).
When they work together, their work rates are additive. So, the combined work rate of Khalil and Teddy is 1/10 + 1/8.
To calculate this combined work rate, we can use a rational equation:
1/10 + 1/8 = (8 + 10) / (10 * 8) = 18/80
Now, to find the time it would take them to complete a one-hour presentation if they worked together, we can calculate the reciprocal of the combined work rate:
(1 hour) / (18/80) = 80/18 ≈ 4.44 hours
Therefore, the correct answer is 4.44 hours.