Question

Kristen can type a 50-page paper in 8 hours. Last month, Kristen and Courtney typed a 50-page paper in 6 hours. How long would it take Courtney to type a 50-page paper on her own

Answer 1

To find out how long it would take Courtney to type a 50-page paper on her own, we use the collective work rate and Kristen's individual rate to establish an equation. The solution to this equation shows that Courtney would take 24 hours to type the paper by herself.

Step-by-step explanation:

This problem involves the rate at which two individuals can complete a typing task and is a typical work rate problem. Kristen can type a 50-page paper on her own in 8 hours. When Kristen and Courtney work together, they can type the same paper in 6 hours. To find out how long it would take for Courtney to type a 50-page paper on her own, we can set up a rate equation based on the given information.

Let's define the rates at which Kristen and Courtney work as K and C respectively, with K being 1/8 (since Kristen types one paper in 8 hours) and C being Courtney's rate of typing a paper in hours. When they work together, their combined rate is 1/6 (since together they type one paper in 6 hours).

The equation is thus: K + C = 1/6
We know K = 1/8, so we substitute in the equation:
1/8 + C = 1/6
C = 1/6 - 1/8
C = 4/24 - 3/24
C = 1/24

Therefore, Courtney's rate is 1/24, meaning she would take 24 hours to type the 50-page paper by herself.

Answer 2

24 hours

Step-by-step explanation:

Kristen = 8 hours

Kristen and Courtney = 6 hours

Courtney = x hours

in six hours kirsten can do 6/8 of the job

6/8 = 3/4

So kirsten is going to be doing 3/4 of the job

Courtney is only going to do 1/4 of the job

Number of hours it takes Courtney to do the job

6/x = 1/4

Cross product

6 * 4 = x * 1

24 = x

x = 24 hours

It will take Courtney 24 hours to type a 50-page paper on her own