Joseph had to type an article containing 10,000 words. How many minutes did it take him? (1) Joseph and Kelly together can type a 75,000-word article in an hour and a half. (2) Joseph types twice as fast as Kelly does.

Joseph take 18 minute to type 10,000 words

Step-by-step explanation:

Given Data

J (Joseph) and K (Kelly) together type=75,000 words at 90 minutes

Means J+K=75,000 at 90 minutes

Joseph types twice of Kelly

Means J=2xK

To find

Joseph type = 10000 words at time=? minutes

Solution

J+K=75,000

As we Known J=2xK

So

2K+K=75,000

K=75,000/3

K=25,000 Means Kelly typed 25,000 words out of 75,000

J=75,000-25,000

J=50,000 Means Joseph typed 50,000 words out of 75,000

So Joseph Typed 50,000 words at 90 minutes and each word time taken as

J=50,000/90

Joseph typed=555.5 words per minute

Now For Joseph type 10,000 words at time

J=10,000/555.5

Joseph Time taken=18 minutes to type 10000 words

0.3 hour or 18 minutes

Step-by-step explanation:

Kelly types half as fast as Joseph, so in the time it takes Joseph to type 10,000 words, Kelly can type 5000. That means they can type 15,000 words working together for that time. We are given their "working together" typing speed, so we can write the proportion ...

(time for 15000 words) / (15000 words) = 1.5 hours / (75000 words)

Multiplying by 15000 gives ...

(time for 15000 words) = (1.5 hours) * (15000/75000) = 1.5/5 hours

time for 15000 words = 0.3 hours = 18 minutes

Joseph can type a 10,000 word article in 0.3 hours, or 18 minutes.