It takes 30mins for 5 old printers to produce a batch of magazines
it takes 16mins for 4 new printers to produce an identical batch of magazines
which of the following would produce a batch of magazines in less time; 6 old printers or 2 new printers
how much less time would this take?
To find out which option would produce a batch of magazines in less time, we need to compare the production rates of the old and new printers.
The old printers produce a batch in 30 minutes, which means they can produce (60/30) = 2 batches per hour.
The new printers produce a batch in 16 minutes, which means they can produce (60/16) = 3.75 batches per hour.
To determine which option would be faster, we compare the number of batches that can be produced:
- 6 old printers can produce 2 * 6 = 12 batches per hour.
- 2 new printers can produce 3.75 * 2 = 7.5 (or 7) batches per hour.
Therefore, 6 old printers would produce a batch of magazines in less time than 2 new printers.
To calculate the time difference, we compare the production rates:
The old printers take 30 minutes to produce a batch.
The new printers take 16 minutes to produce a batch.
The time difference would be 30 - 16 = 14 minutes.
Therefore, using 6 old printers instead of 2 new printers would take 14 minutes less to produce a batch of magazines.
To determine which option would produce a batch of magazines in less time, we can compare the rates at which each option produces the magazines.
First, we calculate the rate at which the old printers produce magazines:
Old printers: 5 printers in 30 minutes
Rate of old printers: 5/30 printers per minute = 1/6 printers per minute
Next, we calculate the rate at which the new printers produce magazines:
New printers: 4 printers in 16 minutes
Rate of new printers: 4/16 printers per minute = 1/4 printers per minute
Now, let's analyze each option:
1. 6 old printers:
Rate of 6 old printers: (1/6) * 6 = 1 printer per minute
2. 2 new printers:
Rate of 2 new printers: (1/4) * 2 = 1/2 printer per minute
Comparing the rates, the 2 new printers produce magazines at a faster rate than the 6 old printers.
To determine how much less time it would take, we can compare the time taken to produce one batch of magazines using each option.
For 6 old printers:
Time taken = 1 / (1/6) = 6 minutes
For 2 new printers:
Time taken = 1 / (1/2) = 2 minutes
Therefore, using 2 new printers would take 4 minutes less (6 - 2 = 4) than using 6 old printers to produce a batch of magazines.
To find out which option would produce a batch of magazines in less time and how much less time it would take, we need to compare the rates of production for each option. Let's calculate the rates first.
The rate of production for the old printers is 5 printers per 30 minutes, which can be expressed as 5/30 printers per minute. Simplifying this, we get 1/6 printers per minute.
The rate of production for the new printers is 4 printers per 16 minutes, which can be expressed as 4/16 printers per minute. Simplifying this, we get 1/4 printers per minute.
Now, let's compare the rates:
For 6 old printers, the rate of production would be (6/6) printers per minute, which is equivalent to 1 printer per minute.
For 2 new printers, the rate of production would be (2/4) printers per minute, which is equivalent to 1/2 printer per minute.
Comparing these rates, 1 printer per minute is faster than 1/2 printer per minute.
Therefore, 6 old printers would produce a batch of magazines in less time compared to 2 new printers.
To calculate the time difference, we need to find the time it takes for each option to produce one batch of magazines.
For 6 old printers, it would take 1 minute to produce a batch of magazines.
For 2 new printers, it would take (1 / (1/2)) = 2 minutes to produce a batch of magazines.
Thus, using 6 old printers instead of 2 new printers would save (2 - 1) = 1 minute of production time.