If x men working x hours per day can do x units of work in x days, then y men working y hours per day in y days would be able to do k units of work. What is the value of k?

  1. A. x^{2}y^{-3}
  2. B. x^{3}y^{-2}
  3. C. y^{2}x^{-3}
  4. D. y^{3}x^{-2} ✓

Correct Answer: D. y^{3}x^{-2}

Explanation

Applying the work equivalence formula \frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}, we get \frac{x \times x \times x}{x} = \frac{y \times y \times y}{k}. This gives x^2 = \frac{y^3}{k}, so k = \frac{y^3}{x^2} = y^3 x^{-2}.

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