14. 10 women can complete a piece of work in 8 days and 10 children take 12 days to complete the same work. How many days will 6 women and 3 children working together take to complete the same piece of work? $$ \begin{array}{lllll} ext { 1) } 2 ext { days } & ext { 2) } 6 ext { days } & ext { 3) } 10 ext { days } & ext { 4) } 12 ext { days } & ext { 5) } 15 ext { days }\end{array} $$

Question

14. 10 women can complete a piece of work in 8 days and 10 children take 12 days to complete the same work. How many days will 6 women and 3 children working together take to complete the same piece of work? $$ \begin{array}{lllll}	ext { 1) } 2 	ext { days } & 	ext { 2) } 6 	ext { days } & 	ext { 3) } 10 	ext { days } & 	ext { 4) } 12 	ext { days } & 	ext { 5) } 15 	ext { days }\end{array} $$

UpStudy AI · Accepted Answer

To determine how many days 6 women and 3 children will take to complete the work, let's break down the problem step by step.

1. **Determine the Work Rate for Women and Children:**
   - **Women:**  
     10 women can complete the work in 8 days.  
     Therefore, the work done by one woman in one day, $$ W $$, is:  
     $$
     10W \times 8 = 1 \quad \Rightarrow \quad W = \frac{1}{80}
     $$
   - **Children:**  
     10 children can complete the work in 12 days.  
     Therefore, the work done by one child in one day, $$ C $$, is:  
     $$
     10C \times 12 = 1 \quad \Rightarrow \quad C = \frac{1}{120}
     $$

2. **Calculate the Combined Daily Work Rate of 6 Women and 3 Children:**
   $$
   \text{Daily work} = 6W + 3C = 6 \times \frac{1}{80} + 3 \times \frac{1}{120}
   $$
   $$
   = \frac{6}{80} + \frac{3}{120} = \frac{3}{40} + \frac{1}{40} = \frac{4}{40} = \frac{1}{10}
   $$
   This means that together, they complete $$\frac{1}{10}$$ of the work each day.

3. **Determine the Total Time to Complete the Work:**
   $$
   \text{Total days} = \frac{1}{\text{Daily work}} = \frac{1}{\frac{1}{10}} = 10 \text{ days}
   $$

**Answer:**  
3) 10 days
6 women and 3 children will take 10 days to complete the work.

10 women can complete a piece of work in 8 days and 10 children take 12 days to complete the
same work. How many days will 6 women and 3 children working together take to complete the
same piece of work?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Arithmetic Questions