If one clerk can process 75 pieces of mail in 2 and 1/2 hours, how long will it take eight clerks to process 1620 pieces of mail if all of them work at this same rate?
75/2.5 = 30
Each clerk can process 30 pieces of mail in an hour.
1620 / (8 * 30) = 6.75 hours
81 hours
To solve this problem, we first need to find the rate at which one clerk processes mail per hour.
We know that one clerk can process 75 pieces of mail in 2 and 1/2 hours. To convert 2 and 1/2 hours to a decimal, we can multiply the whole number (2) by 60 (since there are 60 minutes in an hour) and add it to the fractional part (1/2) times 60 to get the number of minutes.
2 and 1/2 hours = (2 * 60) + (1/2 * 60) = 120 + 30 = 150 minutes
So, one clerk can process 75 pieces of mail in 150 minutes. Now, let's find the rate per hour:
Rate per hour = (75 pieces) / (150 minutes) * (60 minutes / 1 hour) = 75 / 150 * 60 = 30 pieces per hour
Now that we know the rate at which one clerk processes mail, we can calculate how long eight clerks will take to process 1620 pieces of mail.
Total time = (Total number of pieces) / (Rate per hour * Number of clerks)
Total time = 1620 / (30 * 8) = 1620 / 240 = 6.75 hours
Therefore, it will take eight clerks a total of 6.75 hours to process 1620 pieces of mail if all of them work at the same rate.