If 7 men or 10 women can make a 100 meters wall in 10 days, in how many days 14 men and 20 women can make a 600 m wall?

Options

A. 12 days
B. 10 days
C. 18 days
D. 15 days

Answer

To solve the problem step by step, we need to determine how many days it will take for 14 men and 20 women to build a 600-meter wall, given that 7 men or 10 women can build a 100-meter wall in 10 days.

### Step 1: Determine the work rate of men and women
- **Given**:
- 7 men can build a 100-meter wall in 10 days.
- 10 women can build a 100-meter wall in 10 days.

**Work done by men**:
- In 10 days, 7 men build 100 meters.
- Therefore, the work done by 1 man in 10 days = 100 meters / 7 = approximately 14.29 meters.
- Work done by 1 man in 1 day = 14.29 meters / 10 = 1.429 meters.

**Work done by women**:
- In 10 days, 10 women build 100 meters.
- Therefore, the work done by 1 woman in 10 days = 100 meters / 10 = 10 meters.
- Work done by 1 woman in 1 day = 10 meters / 10 = 1 meter.

### Step 2: Calculate the combined work rate of 14 men and 20 women
- Work done by 14 men in 1 day = 14 * 1.429 = 20 meters (approximately).
- Work done by 20 women in 1 day = 20 * 1 = 20 meters.
- Total work done by 14 men and 20 women in 1 day = 20 + 20 = 40 meters.

### Step 3: Determine how many days it will take to build a 600-meter wall
- Total work required = 600 meters.
- Work done in 1 day by 14 men and 20 women = 40 meters.
- Number of days required = Total work / Work done in 1 day = 600 meters / 40 meters per day = 15 days.

### Conclusion
It will take 14 men and 20 women a total of **15 days** to build a 600-meter wall.

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