A mailman can sort out 738 letters in 6 hours. If the number of sorted letters varies directly as the number of working hours, how many letters can be sorted out in 9 hours?
To solve this problem, we can set up a proportion to find the number of letters that can be sorted out in 9 hours.
Let's start by writing our proportion:
Number of letters sorted / Number of hours = Constant
Based on the information given, we know that a mailman can sort out 738 letters in 6 hours. Using this information, we can set up the proportion:
738 letters / 6 hours = x letters / 9 hours
To find x, we can cross multiply and solve for x:
738 * 9 = 6 * x
6622 = 6x
Divide both sides by 6:
x = 6622 / 6
x ≈ 1103
Therefore, the mailman can sort out approximately 1103 letters in 9 hours.
To find out how many letters can be sorted out in 9 hours, we need to use the concept of direct variation. Direct variation means that when one quantity increases, the other quantity also increases by the same proportion.
In this case, we are given that the number of sorted letters varies directly as the number of working hours. We know that the mailman can sort out 738 letters in 6 hours. So, let's set up a proportion to solve the problem:
(738 letters) / (6 hours) = (x letters) / (9 hours)
To solve for x, we can cross multiply:
(738 letters) * (9 hours) = (6 hours) * (x letters)
Simplifying this equation:
6620 letters = 6x letters
Now, we can solve for x:
x = 6620 letters / 6
x = 1103.33 letters
Therefore, the mailman can sort out approximately 1103 letters in 9 hours.