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Let's break down and solve the two parts of the problem:

### 1. **Overtime, Time Rate, and Piece Rate:**

We are asked to calculate the total wages for a worker based on the following information:
- **Hours worked**: 48 hours total (4 hours were overtime and 4 hours were idle due to machine breakdown).
- **Rate per hour**: P20.00 per hour.
- **Overtime pay**: 50% extra (i.e., overtime rate is 1.5 times the regular rate).

#### Solution:

- **Regular hours**: 
  - 44 hours total (48 hours - 4 hours overtime).
  - But since 4 hours were idle, the effective working hours for regular time are 40 hours.
  
- **Overtime hours**: 
  - 4 hours.
  
- **Idle time**: 
  - 4 hours (indirect labor, which isn't paid if it's due to machine breakdown).

##### Wage Calculation:
- **Regular pay** = 40 hours × P20/hour = **P800**.
- **Overtime pay** = 4 hours × P20/hour × 1.5 = **P120**.
- **Total wage** = P800 (regular pay) + P120 (overtime pay) = **P920**.

**Answer for Question 1: Total wage = P920.**

---

### 2. **Time Rate and Piece Rate Calculation:**

We are given that Tom, David, and Harry process tuna fish for the company, and the two payment options are:
- **Piece rate**: P25.00 per tuna fish processed.
- **Time rate**: P50.00 per hour.
- They work 6 hours a day (from 9:00 am to 3:00 pm), 5 days a week.

#### Employee Output:
- Tom processed 60 tuna.
- David processed 52 tuna.
- Harry processed 68 tuna.

#### Solution:

##### (i) **Time Rate System**:
- **Total hours worked per month**:
  - 6 hours/day × 5 days/week × 4 weeks = **120 hours per month**.

For all employees:
- **Monthly wage under time rate** = 120 hours × P50/hour = **P6,000**.

##### (ii) **Piece Rate System**:
- **Tom's wage** = 60 tuna × P25/tuna = **P1,500**.
- **David's wage** = 52 tuna × P25/tuna = **P1,300**.
- **Harry's wage** = 68 tuna × P25/tuna = **P1,700**.

**Answer for Question 2**:

- **Time Rate System**: All employees earn **P6,000** per month.
- **Piece Rate System**: 
  - Tom earns **P1,500**.
  - David earns **P1,300**.
  - Harry earns **P1,700**.

---

Let me know if you would like more details or have any questions. Here are some related questions:

1. What happens if overtime pay is also included for piece-rate workers?
2. How would indirect labor (idle time) affect the overall company's cost?
3. How can you compare efficiency between piece-rate and time-rate systems?
4. If the rates change, how does that impact each payment method?
5. How can a bonus structure be added to incentivize higher productivity?

**Tip**: It's useful to compare time rate vs. piece rate for identifying which system incentivizes productivity better.

An analysis of a time card of a worker shows that out of 48 hours worked, 4 were overtime, and 4 hours were idle due to machine breakdown. The worker earns P20.00 per hour, with overtime paid at 50% extra. You are required to calculate total wages paid to the worker, indicating reasons. Additionally, three workers (Tom, David, and Harry) process tuna for a company with two pay systems: P25 per tuna processed or P50 per hour for 6 hours daily. You are asked to calculate wages for both payment systems.

Learn how to calculate total wages for a worker who worked 48 hours, including overtime and idle time, with a wage rate of P20.00 per hour. Also, compare time and piece rate pay systems for tuna processing employees. Suitable for students in Grades 10-12.

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