15. 2 men and 3 women working together can finish a piece of work in 10 days, while 4 men working together can do it in 10 days. In how many days will 3 men and 3 women working together finish the job? $$ \begin{array}{lllll} ext { 1) } 8 ext { days } & ext { 2) } 10 ext { days } & ext { 3) } 11 ext { days } & ext { 4) } 12 ext { days } & ext { 5) } 15 ext { days }\end{array} $$

Question

15. 2 men and 3 women working together can finish a piece of work in 10 days, while 4 men working together can do it in 10 days. In how many days will 3 men and 3 women working together finish the job? $$ \begin{array}{lllll}	ext { 1) } 8 	ext { days } & 	ext { 2) } 10 	ext { days } & 	ext { 3) } 11 	ext { days } & 	ext { 4) } 12 	ext { days } & 	ext { 5) } 15 	ext { days }\end{array} $$

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

**Given:**
1. **2 men + 3 women** can finish the work in **10 days**.
2. **4 men** can finish the same work in **10 days**.

**Let:**
- $$ m $$ = work rate of one man per day
- $$ w $$ = work rate of one woman per day
- $$ W $$ = total work

**From the second statement:**
$$ 4m \times 10 = W $$
$$ 40m = W $$
$$ m = \frac{W}{40} $$

**From the first statement:**
$$ (2m + 3w) \times 10 = W $$
$$ 20m + 30w = W $$

Substitute $$ W = 40m $$ into the equation:
$$ 20m + 30w = 40m $$
$$ 30w = 20m $$
$$ w = \frac{2}{3}m $$

**Now, find the time for 3 men and 3 women:**
$$ 3m + 3w = 3m + 3\left(\frac{2}{3}m\right) = 3m + 2m = 5m $$

The rate of 3 men and 3 women working together is $$ 5m $$ per day.

**Total work $$ W = 40m $$.**

**Time required:**
$$ \text{Time} = \frac{W}{\text{Rate}} = \frac{40m}{5m} = 8 \text{ days} $$

**Answer:** 
1) 8 days
3 men and 3 women can finish the job in 8 days.

2 men and 3 women working together can finish a piece of work in 10 days, while 4 men working
together can do it in 10 days. In how many days will 3 men and 3 women working together finish
the job?

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