Alice worked 36 hours at regular pay, and 3 fraction numerator 2 over denominator 3 end fraction hours at 1 fraction numerator 1 over denominator 2 end fraction pay. How many equivalent regular hours will Alice be paid in total?

Answer 1

To find out how many equivalent regular hours Alice will be paid, we need to consider both her regular hours and the hours worked at a higher pay rate.

1. Regular hours: Alice worked 36 hours at regular pay. These hours are already equivalent to regular hours, so we can simply count them: \[ \text{Regular hours} = 36 \text{ hours} \]

2. Fractional hours at higher pay: Alice worked \( \frac{2}{3} \) hours at \( \frac{1}{2} \) pay. To convert these hours into equivalent regular hours, we need to determine how many regular hours they represent.

   Since she is making \( \frac{1}{2} \) pay for the \( \frac{2}{3} \) hours worked, we can find the equivalent regular hours using the formula: \[ \text{Equivalent regular hours} = \text{Hours worked} \div \text{Pay rate relative to regular} \] Here, her pay rate is \( \frac{1}{2} \), so: \[ \text{Equivalent regular hours} = \frac{2}{3} \div \frac{1}{2} = \frac{2}{3} \times 2 = \frac{4}{3} \text{ hours} \]

3. Total equivalent regular hours: Now, we can add the regular hours and the equivalent regular hours from the higher pay rate: \[ \text{Total equivalent regular hours} = 36 + \frac{4}{3} \]

   To add these, we need a common denominator. Converting 36 to a fraction gives: \[ 36 = \frac{108}{3} \]

   Therefore: \[ \text{Total equivalent regular hours} = \frac{108}{3} + \frac{4}{3} = \frac{108 + 4}{3} = \frac{112}{3} \]

   Converting \(\frac{112}{3}\) back to decimal gives: \[ \frac{112}{3} \approx 37.33 \text{ hours} \]

Thus, the total number of equivalent regular hours Alice will be paid is: \[ \boxed{\frac{112}{3}} \text{ or approximately } 37.33 \text{ hours.} \]

Answer 2

the extra hours are paid at 1 1/2 times the normal rate, not 1/2. You should know that overtime pay is higher than regular pay. Also, he worked 3 2/3 hrs extra. You need to learn how to interpret fractions and mixed numbers types by clueless users.

36 + (3 2/3)*(1 1/2) = 41 1/2 equivalent hours.

Answer 3

Thank you for your clarification. Let’s revise the calculations with the correct interpretation of the pay rate and the extra hours worked:

1. Regular hours: Alice worked 36 hours at regular pay. Therefore: \[ \text{Regular hours} = 36 \text{ hours} \]

2. Extra hours: Alice worked \(3 \frac{2}{3}\) hours at \(1 \frac{1}{2}\) times the regular pay. We will convert the mixed numbers to improper fractions:

   • \(3 \frac{2}{3} = \frac{11}{3}\) hours
   • \(1 \frac{1}{2} = \frac{3}{2}\) times the regular rate

3. Converting extra hours to equivalent regular hours: To find the equivalent regular hours for the extra hours worked, we multiply the number of extra hours by the overtime pay rate: \[ \text{Equivalent regular hours from extra hours} = \left(\frac{11}{3}\right) \times \left(\frac{3}{2}\right) \]

   Performing the multiplication: \[ = \frac{11 \times 3}{3 \times 2} = \frac{33}{6} = \frac{11}{2} = 5 \frac{1}{2} \text{ hours} \]

4. Total equivalent regular hours: Now we add the regular hours and the equivalent hours from the extra hours: \[ \text{Total equivalent regular hours} = 36 + 5 \frac{1}{2} \]

   Converting \(5 \frac{1}{2}\) to an improper fraction: \[ 5 \frac{1}{2} = \frac{11}{2} \]

   Now converting 36 to a fraction for adding: \[ 36 = \frac{72}{2} \]

   Now we add the two fractions: \[ \text{Total} = \frac{72}{2} + \frac{11}{2} = \frac{72 + 11}{2} = \frac{83}{2} \]

   This can also be converted back to a mixed number if needed: \[ \frac{83}{2} = 41 \frac{1}{2} \text{ hours} \]

Thus, the total number of equivalent regular hours that Alice will be paid is: \[ \boxed{41 \frac{1}{2}} \text{ hours.} \]

Thank you for your patience and for pointing out the discrepancies!