Final answer:
By determining the work rates of men, women, and children separately, and then combining their rates, it's deduced that 2 men, 4 women, and 10 children working together can complete a piece of work in approximately 1.11 days, which is rounded up to 1 day.
Step-by-step explanation:
To solve the problem, let's find the work rate of each group and then combine them to find the rate at which they can complete the work together. We know that 4 men can complete the work in 2 days, so the rate of men's work is 1/2 work per day (0.5 work/day). Similarly, 4 women can complete the work in 4 days, so their rate is 1/4 work per day (0.25 work/day), and 5 children can complete the work in 4 days, which means their rate is 1/5 work per day (0.2 work/day).
Next, we calculate the rate of 2 men, 4 women, and 10 children working together:
- 2 men: 2 men * (0.5 work/day / 4 men) = 0.25 work/day
- 4 women: 4 women * (0.25 work/day / 4 women) = 0.25 work/day
- 10 children: 10 children * (0.2 work/day / 5 children) = 0.4 work/day
The combined rate is 0.25 work/day + 0.25 work/day + 0.4 work/day = 0.9 work/day. Therefore, the group of 2 men, 4 women, and 10 children can complete the work in 1/0.9 days, which is approximately 1.11 days.
Since they cannot complete the work in less than a day, the total time needed will be rounded up to 1 day.