1) It takes a team of 3 painters 22 days tho paint a house. a) How long would it take 10 painters to paint the same house? b) How many painters would be needed in order to paint the same house in 11 days Solutions to Exercise 4 number I are on page 256

Sure, let's solve the given problems step by step. ### **Problem Statement** 1) It takes a team of **3 painters 22 days** to paint a house. a) **How long would it take 10 painters to paint the same house?** b) **How many painters would be needed to paint the same house in 11 days?** --- ### **Understanding the Concept** This problem involves the concept of **work rate**, where the total amount of work done is a product of the number of workers and the time they take to complete the work. The relationship can be described by the formula: \[ \text{Work} = \text{Number of Workers} \times \text{Time} \] Since the amount of work (painting the house) remains constant, we can set up the equation based on this principle. --- ### **Given Data** - **Number of Painters (Initial)**, \( P_1 = 3 \) painters - **Time Taken (Initial)**, \( T_1 = 22 \) days --- ### **a) Time Required for 10 Painters** **Find:** \( T_2 \) when \( P_2 = 10 \) painters 1. **Calculate Total Work:** \[ \text{Work} = P_1 \times T_1 = 3 \times 22 = 66 \text{ painter-days} \] 2. **Calculate Time for 10 Painters:** \[ T_2 = \frac{\text{Work}}{P_2} = \frac{66}{10} = 6.6 \text{ days} \] **Answer:** It would take **6.6 days** for 10 painters to paint the house. --- ### **b) Number of Painters Needed to Complete in 11 Days** **Find:** \( P_2 \) when \( T_2 = 11 \) days 1. **Calculate Total Work (Same as above):** \[ \text{Work} = 66 \text{ painter-days} \] 2. **Calculate Number of Painters Needed:** \[ P_2 = \frac{\text{Work}}{T_2} = \frac{66}{11} = 6 \text{ painters} \] **Answer:** **6 painters** are needed to paint the house in 11 days. --- ### **Summary of Answers** a) **6.6 days** for 10 painters. b) **6 painters** needed to complete the job in 11 days. ---