A wall of 100 metres can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 metres?

### Concept & Extended Chain Rule When "or" establishes an efficiency relationship and the total work output (meters of wall) changes, we combine the efficiency conversion with the extended chain rule. $$ \frac{M_1 D_1}{W_1} = \frac{M_2 D_2}{W_2} $$ ### Step-by-Step Solution * Find the efficiency relationship: 7 men = 10 women. * Determine the workforce for scenario 2: 14 men and 20 women. * Convert the target workforce into a single unit (men): Since 10 women = 7 men, then 20 women = 14 men. * Total equivalent men for scenario 2: $14 \text{ men} + 14 \text{ men} = 28 \text{ men}$. * Identify variables for the formula: $M_1 = 7 \text{ men}$, $D_1 = 10 \text{ days}$, $W_1 = 100 \text{ m}$ $M_2 = 28 \text{ men}$, $D_2 = x \text{ days}$, $W_2 = 600 \text{ m}$ * Substitute into the formula: $$ \frac{7 \times 10}{100} = \frac{28 \times x}{600} $$ * Simplify the left side: $\frac{70}{100} = 0.7$. * Simplify the right side denominator: multiply both sides by 600. $$ 0.7 \times 600 = 28 \times x $$ $$ 420 = 28x $$ * Solve for $x$: $x = \frac{420}{28} = 15 \text{ days}$. ### Exam Strategy & Shortcut Observe the direct multipliers. The workforce changes from 7 men to an equivalent of 28 men (which is a 4x increase in workforce). 4x the workforce means they work 4x as fast, or do 4x the work in the same time. In 10 days, this 4x workforce would build $100 \text{ m} \times 4 = 400 \text{ m}$. To build 600m (which is 1.5x of 400m), they need $10 \text{ days} \times 1.5 = 15 \text{ days}$. ### Common Pitfall A frequent error is forgetting to put the length of the wall (the "work") in the denominator and treating it as a direct multiplier in the numerator instead. ### Final Answer Therefore, the correct answer is **15**.