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?
L = 738/6h * 9h =
To solve this problem, we can set up a proportion:
number of letters / number of hours = number of letters / number of hours
Let's call the number of letters sorted out in 9 hours "x."
Using the given information, we can set up the proportion:
738 letters / 6 hours = x letters / 9 hours
Now, we need to solve for "x."
Cross-multiplying, we get:
6 hours * x letters = 738 letters * 9 hours
6x = 6642
Dividing both sides by 6, we find:
x = 1107
So, a mailman can sort out 1107 letters in 9 hours.
To find the number of letters that can be sorted out in 9 hours, we need to use the concept of direct variation. In this case, we know that the number of sorted letters varies directly as the number of working hours.
Direct variation can be expressed using the equation: y = kx, where y is the dependent variable (the number of sorted letters), x is the independent variable (the number of working hours), and k is the constant of variation (the rate of change).
To find the value of k, we can use the given information that a mailman can sort out 738 letters in 6 hours.
So, we have:
738 = k * 6
To find k, we divide both sides of the equation by 6:
k = 738 / 6
k = 123
Now that we have the constant of variation (k), we can use it to find the number of letters that can be sorted out in 9 hours.
Let's assign x as 9 (the number of working hours) and solve for y (the number of sorted letters):
y = k * x
y = 123 * 9
Calculating:
y = 1107
Therefore, in 9 hours, the mailman can sort out 1107 letters.