An assembly line moves at a rate of 25 object permanence after one minute the rate goes up by two objects per minute for six minutes, then slows down for for objects per minute for nine minutes before resuming normal speed how many objects pass a worker station on the line during the last one half hour?
To solve this problem, we'll break it down step by step.
Step 1: Calculate the number of objects that move at a normal speed:
Rate of objects moving at normal speed = 25 objects/minute * 30 minutes = 750 objects
Step 2: Calculate the number of objects that move at an increased rate for 6 minutes:
Rate of objects moving at increased rate = (25 objects/minute + 2 objects/minute) * 6 minutes = 162 objects
Step 3: Calculate the number of objects that move at a slowed rate for 9 minutes:
Rate of objects moving at slowed rate = (25 objects/minute - 4 objects/minute) * 9 minutes = 189 objects
Step 4: Calculate the total number of objects that pass the worker station during the last half hour:
Total number of objects = Normal speed objects + Increased rate objects + Slowed rate objects
Total number of objects = 750 objects + 162 objects + 189 objects = 1101 objects
Therefore, during the last half hour, 1101 objects will pass a worker station on the assembly line.
To find out how many objects pass a worker station on the line during the last half-hour, we need to break down the time intervals and calculate the number of objects passing in each interval.
1. Normal speed for the first minute:
The assembly line moves at a rate of 25 objects per minute, so 25 objects pass the worker station in the first minute.
2. Increased speed for six minutes:
For the next six minutes, the rate goes up by two objects per minute. So, for each minute, the number of objects passing the worker station increases by 2. We can calculate the total number of objects passed in these six minutes using the formula for the sum of an arithmetic series:
Number of objects = (First term + Last term) * Number of terms / 2
First term = 25
Last term = 25 + 2 * 6 = 37
Number of terms = 6
Number of objects = (25 + 37) * 6 / 2 = 62 * 6 / 2 = 372 / 2 = 186 objects
3. Slower speed for nine minutes:
For the next nine minutes, the rate slows down to four objects per minute. So, the number of objects passing the worker station each minute is 4. We can calculate the total number of objects passed in these nine minutes:
Number of objects = Rate * Time = 4 objects/min * 9 min = 36 objects
4. Normal speed for the remaining time:
The last half-hour is equivalent to 30 minutes. So, the assembly line moves at the normal speed of 25 objects per minute for this duration. We can calculate the total number of objects passed in these 30 minutes:
Number of objects = Rate * Time = 25 objects/min * 30 min = 750 objects
Finally, we can find the total number of objects passing the worker station during the last half-hour by adding up the number of objects from each interval:
Total number of objects = 25 + 186 + 36 + 750 = 997 objects
Therefore, 997 objects pass the worker station on the line during the last half-hour.
To find the number of objects that pass a worker station on the assembly line during the last half hour, we need to break down the problem into smaller time intervals and calculate the number of objects passing the worker station in each interval.
Let's go step by step:
1. Normal Speed (First 1 minute): The assembly line moves at a rate of 25 objects per minute. So, in the first 1 minute, 25 objects pass the worker station.
2. Increased Speed (Next 6 minutes): The rate of the assembly line increases by two objects per minute. So, in the next 6 minutes, the rate becomes 25 + (2 * 6) = 37 objects per minute. Therefore, in these 6 minutes, 37 * 6 = 222 objects pass the worker station.
3. Slowing Down (Next 9 minutes): The rate of the assembly line slows down by four objects per minute. So, in the next 9 minutes, the rate becomes (37 - 4) = 33 objects per minute. Therefore, in these 9 minutes, 33 * 9 = 297 objects pass the worker station.
4. Resumed Normal Speed (Remaining time): The assembly line continues at the normal speed for the remaining time, which is the last half hour. In one hour, there are 60 minutes. So, the last half hour is 60/2 = 30 minutes. At the normal speed of 25 objects per minute, in 30 minutes, 25 * 30 = 750 objects pass the worker station.
Now, we add up the objects passing the worker station for each time interval:
25 (first minute) + 222 (increased speed) + 297 (slowed down) + 750 (last half hour) = 1,294 objects.
Therefore, during the last half hour, a total of 1,294 objects pass the worker station on the assembly line.