A group of five clerks has been assigned to insert 24,000 letters into envelopes. The clerks perform this work at the following rates of speed: Clerk A, 1100 letters an hour; Clerk B, 1450 letters an hour; Clerk C, 1200 letters an hour; Clerk D, 1300 letters an hour; Clerk E, 1250 letters an hour. At the end of two hours of work, Clerk C and D are assigned to another task. From the time that Clerks C and D were taken off the assignment, the number of hours required for the remaining clerks to complete this assignment is?
Answer: More than 2 hr, but less than 4 hr
Explanation
To solve this problem, we can follow these steps:
1. Calculate the total number of letters inserted by all clerks in 2 hours:
- Clerk A: 1100 letters/hour × 2 hours = 2200 letters
- Clerk B: 1450 letters/hour × 2 hours = 2900 letters
- Clerk C: 1200 letters/hour × 2 hours = 2400 letters
- Clerk D: 1300 letters/hour × 2 hours = 2600 letters
- Clerk E: 1250 letters/hour × 2 hours = 2500 letters
Total letters inserted in 2 hours:
2200 + 2900 + 2400 + 2600 + 2500 = 12600 letters
2. Determine the remaining letters to be inserted:
- Total letters to be inserted: 24,000
- Letters already inserted: 12,600
Remaining letters: 24,000 - 12,600 = 11,400 letters
3. Calculate the rate of the remaining clerks (A, B, and E) per hour:
- Clerk A: 1100 letters/hour
- Clerk B: 1450 letters/hour
- Clerk E: 1250 letters/hour
Total rate of A, B, and E:
1100 + 1450 + 1250 = 3800 letters/hour
4. Calculate the time required to insert the remaining letters:
- Time required = Remaining letters / Rate of A, B, and E
- Time required = 11,400 letters / 3800 letters/hour = 3 hours
Answer: More than 2 hr, but less than 4 hr.
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