if 1000 articles of a given type can be returned out by a first machine in 8 hours, by a second in 5 hours, and by the third in 4 hours, how long will it take to turn out the articles with an machine working?
The machines turn our articles at rates 1000/8, 1000/5 and 1000/4 per hour.
Total production rate by all
= 125 + 200 + 250 = 575 articles/hour
575 * t = 1000
t = 1.74 hours
To find out how long it would take for all the machines working together to produce the articles, we need to calculate their combined productivity.
Let's first calculate the productivity of each machine per hour:
- The first machine can produce 1000 articles in 8 hours, so its productivity is 1000/8 = 125 articles per hour.
- The second machine can produce 1000 articles in 5 hours, so its productivity is 1000/5 = 200 articles per hour.
- The third machine can produce 1000 articles in 4 hours, so its productivity is 1000/4 = 250 articles per hour.
Now, let's sum up the productivity of all three machines:
125 articles/hour + 200 articles/hour + 250 articles/hour = 575 articles/hour.
Therefore, all the machines working together can produce 575 articles per hour. To find out how long it will take for them to produce 1000 articles, we can use the formula:
Time = Total articles / Combined productivity
Time = 1000 articles / 575 articles/hour
Time ≈ 1.74 hours
Therefore, it will take approximately 1.74 hours for all the machines working together to produce the articles.