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?
find each machine rate:
rate1=1000/8
rate2=1000/
rate3=1000/4
So I assume you want a combined rate.
rate= number per time
So in forty hours, machine2=1000/8hr*40hrs=5000
machine2=1000/5hr*40hrs =8000
machine3=1000/4hr*40hrs=10000
combined rate=23000/40hrs=575per hour
To find out how long it will take for one machine to produce the given number of articles, we need to calculate the rate of production for each machine and then combine them.
Let's start by calculating the production rate for each machine:
For the first machine, it can produce 1000 articles in 8 hours. So the rate of production for the first machine is 1000 articles / 8 hours = 125 articles per hour.
For the second machine, it can produce 1000 articles in 5 hours. So the rate of production for the second machine is 1000 articles / 5 hours = 200 articles per hour.
For the third machine, it can produce 1000 articles in 4 hours. So the rate of production for the third machine is 1000 articles / 4 hours = 250 articles per hour.
Now, to find out how long it will take for one machine to produce 1000 articles, we need to combine the production rates of the three machines. We do this by adding up their production rates:
Combined production rate = Production rate of first machine + Production rate of second machine + Production rate of third machine
Combined production rate = 125 articles per hour + 200 articles per hour + 250 articles per hour
Combined production rate = 575 articles per hour
Finally, to find out how long it will take for one machine to produce the articles, we divide the total number of articles by the combined production rate:
Time needed = Total number of articles / Combined production rate
Time needed = 1000 articles / 575 articles per hour
Time needed ≈ 1.74 hours (rounded to two decimal places)
Therefore, it will take approximately 1.74 hours for one machine to produce 1000 articles.