An employee worked 11 hours in a day. Her regular working day is 7.5 hours and the rest was overtime, for which she was paid 1.5 times her regular hourly rate. If she was paid $112 for the day, what was her regular rate per hour for that day?
$8.78
If the rate was r, then
7.5r + (11-7.5)(1.5r) = 112
$8.78 x 7.5 = 65.85 (her hourly)
(8.78 x 1.5 = 13.17 (rate time and half))
$13.17 x 3.5 = 46.09 (how much she made working over time for 3.5 hours.
= $111.94 (approx. $112 includes her regular shift + overtime ammount).
Well, it seems like this employee really went the extra mile, or should I say, the extra hours? But don't worry, I won't go the extra mile to solve this riddle for you!
Let's break it down. The employee worked 11 hours in total, and her regular working day is 7.5 hours. That means she worked 3.5 hours of overtime. Since she was paid 1.5 times her regular hourly rate for overtime, we can calculate her regular rate per hour.
Let's assume her regular rate per hour is "x". So, for the regular 7.5 hours, she earned 7.5 times "x". And for the 3.5 hours of overtime, she earned 3.5 times 1.5 times "x" (since it's 1.5 times her regular rate).
Now, we can set up an equation to find "x".
7.5x + 3.5(1.5x) = 112
Let's solve it:
7.5x + 5.25x = 112
12.75x = 112
x = 8.784... (approximately)
So, her regular rate per hour for that day was approximately $8.78. That's the price of going above and beyond!
To solve this problem, we need to break it down into two parts: the regular working hours and the overtime hours.
Step 1: Calculate the regular hours
The employee worked a total of 11 hours and her regular working day is 7.5 hours. Therefore, the difference between these two is the number of overtime hours worked.
Regular hours = Total hours - Overtime hours
Regular hours = 11 hours - Overtime hours
Step 2: Calculate the overtime hours
The overtime hours are the additional hours worked beyond the regular working day. In this case, it is the difference between the total hours worked and the regular working day.
Overtime hours = Total hours - Regular working day
Overtime hours = 11 hours - 7.5 hours
Step 3: Calculate the regular rate per hour
The employee received a total payment of $112 for the day. We can use this information to find the regular rate per hour.
Regular payment = Regular hours x Regular rate per hour
Overtime payment = Overtime hours x (Regular rate per hour x 1.5)
Total payment = Regular payment + Overtime payment
$112 = (Regular hours x Regular rate per hour) + (Overtime hours x (Regular rate per hour x 1.5))
Step 4: Solve for the regular rate per hour
Substituting the values from Steps 1 and 2 into the equation from Step 3, we can solve for the regular rate per hour.
$112 = (11 hours - Overtime hours) x Regular rate per hour + (Overtime hours x (Regular rate per hour x 1.5))
Simplifying the equation further:
$112 = 11 hours x Regular rate per hour - Overtime hours x Regular rate per hour + Overtime hours x (Regular rate per hour x 1.5)
Step 5: Substitute the known values and solve for the regular rate per hour
Substituting the known values into the equation from Step 4, we can solve for the regular rate per hour:
$112 = 11 hours x Regular rate per hour - (11 hours - 7.5 hours) x Regular rate per hour + (11 hours - 7.5 hours) x (Regular rate per hour x 1.5)
$112 = 11 hours x Regular rate per hour - 3.5 hours x Regular rate per hour + 3.5 hours x (Regular rate per hour x 1.5)
$112 = 11 Regular rate per hour - 3.5 Regular rate per hour + 3.5 (Regular rate per hour x 1.5)
$112 = 7.5 Regular rate per hour + 3.5 (Regular rate per hour x 1.5)
Now, we can solve the equation to find the regular rate per hour for that day.