The problem asks to find the wages for 50 hours of work using "time and a half" overtime pay after 40 hours. Here's how to approach it:

Step-by-step explanation:

1. Normal Pay:

   • For the first 40 hours, the worker is paid at a regular rate (denoted as $R$).
   • This means the wages for the first 40 hours = $40 \times R$.

2. Overtime Pay:

   • Overtime starts after 40 hours.
   • The overtime rate is "time and a half," which means the worker earns $1.5 \times R$ for each additional hour worked beyond 40 hours.
   • The worker worked 50 hours, so 10 hours are overtime.
   • The wages for these 10 hours = $10 \times 1.5R = 15R$.

3. Total Wages:

   • The total wages for 50 hours will be: $\text{Total wages} = 40R + 15R = 55R$

Now, based on the table provided, you can find $R$:

• When 10 hours of work (including overtime) are done, the wages are $120. This indicates that $10 \times R = 120$, so: $R = \frac{120}{10} = 12$

Using this value for $R$, calculate the wages for 50 hours of work:

$\text{Total wages} = 55R = 55 \times 12 = 660$

Answer:

The wages for 50 hours of work are $660.

Would you like further details or have any other questions? Here are some related questions for practice:

1. What would the wages be for 45 hours of work?
2. How much overtime pay is earned if 55 hours are worked?
3. How would the wages change if the overtime rate was "double time" instead of "time and a half"?
4. If the worker earns $960 for 60 hours, what is their regular hourly rate?
5. What would happen if the overtime rate started after 35 hours instead of 40 hours?

Tip: Always separate normal hours from overtime hours when calculating wages under different pay rates.