Question

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!