A mail handler needs 3 hours to sort the mail, but with an assistant, it takes 2 hours. How long would it take the assistant to sort the mail working alone?
Let that assitant's time be t.
1/2 = 1/t + 1/3 jobs per hour
1/t = 1/6
t = 6 hours
To find out how long it would take the assistant to sort the mail working alone, we can use the concept of "work rates."
Let's assume that the mail handler's work rate is represented by H (in units of "mail per hour") and the assistant's work rate is represented by A (also in units of "mail per hour").
We know that the mail handler takes 3 hours to sort the mail, which means their work rate is H = 1/3 (1 job done in 3 hours) or 1/3 mail per hour.
When the assistant helps, the combined work rate is H + A = 1/2 (1 job done in 2 hours) or 1/2 mail per hour.
Now, we need to find the assistant's work rate A when working alone.
To do this, we can subtract the mail handler's work rate from the combined work rate:
A = H + A - H
Simplifying, we get:
A = 1/2 - 1/3
The least common denominator of 2 and 3 is 6, so we can rewrite the equation as:
A = 3/6 - 2/6
A = 1/6
Therefore, the assistant's work rate is 1/6 mail per hour.
To determine how long it would take the assistant to sort the mail working alone, we can invert the assistant's work rate:
1 / (1/6) = 6/1
So, it would take the assistant 6 hours to sort the mail working alone.