IF ONE CLERK CAN PROCESS 75 PIECES OF MAIL IN 2 AND A HALF HOURS, HOW LONG WILL ITTAKE EIGHT CLERKS TO PROCESS 1620 PIECESOF MAIL IF ALL OF THEM WORK AT THIS SAME RATE?

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If one clerk can process 75 pieces of mail in 2.5 hours, he/she can process 75/2.5=30 pieces of mail every hour.

With 1620 pieces of mail, and 8 clerks, it will take 1620/(8*30)=6.75 hours.

To solve this problem, we can use the concept of proportionality.

First, let's find the rate at which one clerk processes mail. We know that in 2 and a half hours (or 2.5 hours), one clerk can process 75 pieces of mail. We can use this information to find the rate:

Rate of one clerk = Number of pieces of mail processed / Time taken
Rate of one clerk = 75 pieces / 2.5 hours = 30 pieces/hour

Now, let's determine how long it will take eight clerks to process 1620 pieces of mail, working at the same rate. We can set up a proportion:

(Number of clerks / Time taken) = (Number of pieces of mail / Rate of one clerk)

Let's assign the variable "t" to represent the time taken. Therefore, the equation becomes:

(8 clerks / t hours) = (1620 pieces / 30 pieces/hour)

To solve for "t," we can cross-multiply and then solve for "t":

8t = 1620 * 30
8t = 48600
t = 48600 / 8
t = 6075

Therefore, it will take eight clerks approximately 6075 hours to process 1620 pieces of mail if they all work at the same rate.