A factory produces 12000 plastic bottles by using 3 machines 8 hours a day. One machine is out of order now. The owner wants to produce 15000 plastic bottles, How many hours the remaining machines have to work to produce the required bottles?
3 machines take 8 hours to do 12000 bottles
1 machine takes 24 hours to do 12000 bottle
2 machines take 12 hrs to do 12000 bottles
15000/12000 = 5/4 <--- should take 5/4 times as long
so 2 machines take (12)(5/4) hrs to do 15000 bottles
time taken = 15 hrs
check my arithmetic
Oh no, one of the machines has gone on strike! I guess it finally realized it needed a break too. Anyway, let's crunch some numbers to help the owner out.
So, originally, with 3 machines working for 8 hours, the factory produced 12,000 bottles.
That means, each machine produced 12,000 / (3 * 8) = 500 bottles per hour.
Now, since one machine is out of order, we have two remaining machines. To produce 15,000 bottles, we just need to divide by the new production rate:
15,000 / (2 * x) = 500, where x is the number of hours the machines have to work.
Solving for x, we get x = 15,000 / (2 * 500) = 15 hours.
So, the remaining machines will have to work for 15 hours to produce the required 15,000 bottles. Let's hope they don't develop any machine-related anxiety in the process!
To find the number of hours the remaining machines have to work to produce the required 15000 plastic bottles, we can set up a proportion using the number of machines and the number of bottles produced:
Number of machines available / Number of machines being used = Number of bottles produced / Number of bottles required
Since one machine is out of order, we have 2 machines available. The number of machines being used is still 3, as stated in the question, but one of them is out of order. The number of bottles already produced is 12000, and the number of bottles required is 15000.
So, the proportion becomes:
2 / 3 = 12000 / 15000
To solve this proportion, we can cross-multiply:
2 * 15000 = 3 * 12000
30000 = 36000
Now, we can solve for the missing value, which is the number of hours the remaining machines have to work. Let's call it "x":
x = (30000 * 8) / 12000
x = 20
Therefore, the remaining machines have to work for 20 hours to produce the required 15000 plastic bottles.
To determine the number of hours the remaining machines need to work to produce the required 15,000 plastic bottles, we can use the concept of machine-hours.
Machine-hours refer to the total hours worked by all the machines combined. In this case, initially, there were 3 machines working for 8 hours a day. So, the total machine-hours for a day would be 3 machines x 8 hours = 24 machine-hours.
Now, since one machine is out of order, we have 2 machines available to work. Let's assume these machines work for 'x' hours to produce the required 15,000 plastic bottles.
Using the concept of machine-hours, we can set up the following equation:
2 machines x 'x' hours = 24 machine-hours
To solve for 'x':
2x = 24
x = 24 / 2
x = 12
Therefore, the remaining machines have to work for 12 hours to produce the required 15,000 plastic bottles.