Sam can sort 4000 pieces of mail in 5 hours. With a co-worker they can sort 4000 pieces of mail in 3 hours. How long will it take his co-worker to sort 2000 pieces of mail.
consider 4000 pieces one "job". The classic work problem now becomes
1/5 + 1/x = 1/3
x = 15/2
So, he can sort 2000 mails (1/2 job) in 15/4 hour
To solve this problem, we first need to determine the rate at which Sam and his co-worker can sort mail together.
From the given information, we know that Sam can sort 4000 pieces of mail in 5 hours. Therefore, his rate is 4000/5 = 800 pieces of mail per hour.
Let's denote the co-worker's rate as "C."
We are also given that together, Sam and his co-worker can sort 4000 pieces of mail in 3 hours. Therefore, their combined rate is 4000/3 = 1333.33 pieces of mail per hour.
To find the co-worker's rate, we can subtract Sam's rate from the combined rate:
1333.33 (combined rate) - 800 (Sam's rate) = 533.33 pieces of mail per hour.
Now that we have the co-worker's rate, we can find out how long it will take him to sort 2000 pieces of mail.
Divide the number of pieces of mail (2000) by the co-worker's rate (533.33) to get the time required:
2000 / 533.33 = 3.75 hours.
Therefore, it will take Sam's co-worker 3.75 hours to sort 2000 pieces of mail.