If $7$ maids with $7$ mops cleaned $7$ floors in $7$ hours, how long would it take $3$ maids to mop $3$ floors with $3$ mops?

### Concept & Work Equivalence Formula In problems where workers each have their own tool (like mops), the tool count is redundant information. The relationship is between workers ($M$), time ($T$), and work done ($W$): $$ \frac{M_1 \times T_1}{W_1} = \frac{M_2 \times T_2}{W_2} $$ ### Step-by-Step Solution * **Given**: - $M_1 = 7$ maids, $W_1 = 7$ floors, $T_1 = 7$ hours. - $M_2 = 3$ maids, $W_2 = 3$ floors. * **Calculation**: Substitute values into the formula: $$ \frac{7 \times 7}{7} = \frac{3 \times T_2}{3} $$ $$ 7 = T_2 $$ So, it takes $7$ hours. ### Exam Strategy & Shortcut Recognize that the rate is "$1$ maid cleans $1$ floor in $7$ hours." Therefore, any number of maids cleaning an equal number of floors will always take $7$ hours. ### Common Pitfall Blindly matching the numbers and assuming $3$ maids cleaning $3$ floors takes $3$ hours. Rate does not change linearly like that. ### Final Answer Therefore, the correct answer is **7 hours**.