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There are 4 card-processing machines in an office. The fastest of these machines processes x cards in 7 hours and the slowest processes x cards in 8 hours. Which of the following could NOT be the average time per machine for each of the 4 machines to process x cards?
- a)7.2
- b)7.3
- c)7.5
- d)7.6
- e)7.7
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
There are 4 card-processing machines in an office. The fastest of thes...
The range of possible average times per machine for each of the 4 card-processing machines can be determined by considering the fastest machine, which takes 7 hours to process x cards, and the slowest machine, which takes 8 hours to process x cards.
The maximum possible average time per machine is obtained by assuming that the fastest machine is assigned the maximum processing time of 7 hours, and the other three machines equally share the remaining processing time. In this scenario, the maximum average time per machine is calculated as (8 * 3 + 7) / 4 = 31 / 4 = 7.75.
On the other hand, the minimum possible average time per machine is obtained by assuming that the slowest machine is assigned the maximum processing time of 8 hours, and the other three machines equally share the remaining processing time. In this case, the minimum average time per machine is calculated as (7 * 3 + 8) / 4 = 29 / 4 = 7.25.
Therefore, the average time per machine for each of the 4 machines to process x cards cannot be less than 7.25 hours.
Community Answer
There are 4 card-processing machines in an office. The fastest of thes...
Understanding the Problem
There are 4 card-processing machines with varying speeds. The fastest machine processes x cards in 7 hours, while the slowest takes 8 hours. We need to determine the average time per machine for processing x cards and identify which option cannot be the average.
Processing Rates of Machines
- Fastest Machine:
- Time = 7 hours
- Slowest Machine:
- Time = 8 hours
The two remaining machines must have processing times between 7 and 8 hours.
Average Calculation
To find the average time per machine, we sum the times for all four machines and divide by 4.
- Let:
- Time of the fastest machine = 7 hours
- Time of the slowest machine = 8 hours
- Let the times of the two other machines be T1 and T2 (where 7 < t1,="" t2="" />< />
The average time (A) can be expressed as:
A = (7 + T1 + T2 + 8) / 4
Possible Values for Average Time
- The minimum average occurs when T1 and T2 are both 7 hours, leading to:
- A_min = (7 + 7 + 7 + 8) / 4 = 7.25 hours
- The maximum average occurs when T1 and T2 are both 8 hours, leading to:
- A_max = (7 + 8 + 8 + 8) / 4 = 7.75 hours
Analyzing Options
Given the range of possible averages (7.25 to 7.75 hours), we can analyze the options:
- a) 7.2 - Outside the range (not possible)
- b) 7.3 - Within the range
- c) 7.5 - Within the range
- d) 7.6 - Within the range
- e) 7.7 - Within the range
Conclusion
The only average time that could NOT occur is 7.2 hours, as it falls outside the calculated range of 7.25 to 7.75 hours. Thus, the correct answer is option 'A'.
There are 4 card-processing machines with varying speeds. The fastest machine processes x cards in 7 hours, while the slowest takes 8 hours. We need to determine the average time per machine for processing x cards and identify which option cannot be the average.
Processing Rates of Machines
- Fastest Machine:
- Time = 7 hours
- Slowest Machine:
- Time = 8 hours
The two remaining machines must have processing times between 7 and 8 hours.
Average Calculation
To find the average time per machine, we sum the times for all four machines and divide by 4.
- Let:
- Time of the fastest machine = 7 hours
- Time of the slowest machine = 8 hours
- Let the times of the two other machines be T1 and T2 (where 7 < t1,="" t2="" />< />
The average time (A) can be expressed as:
A = (7 + T1 + T2 + 8) / 4
Possible Values for Average Time
- The minimum average occurs when T1 and T2 are both 7 hours, leading to:
- A_min = (7 + 7 + 7 + 8) / 4 = 7.25 hours
- The maximum average occurs when T1 and T2 are both 8 hours, leading to:
- A_max = (7 + 8 + 8 + 8) / 4 = 7.75 hours
Analyzing Options
Given the range of possible averages (7.25 to 7.75 hours), we can analyze the options:
- a) 7.2 - Outside the range (not possible)
- b) 7.3 - Within the range
- c) 7.5 - Within the range
- d) 7.6 - Within the range
- e) 7.7 - Within the range
Conclusion
The only average time that could NOT occur is 7.2 hours, as it falls outside the calculated range of 7.25 to 7.75 hours. Thus, the correct answer is option 'A'.
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There are 4 card-processing machines in an office. The fastest of these machines processes x cards in 7 hours and the slowest processes x cards in 8 hours. Which of the following could NOT be the average time per machine for each of the 4 machines to process x cards?a)7.2b)7.3c)7.5d)7.6e)7.7Correct answer is option 'A'. Can you explain this answer?
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