Time & Work

Forget fractions ($1/x$). Use Units.

• Method: Assume Total Work = LCM of given days.
• Efficiency (Per Day Work): $\text{Total Work} / \text{Days}$.

Comparing two groups of workers.

• Formula: $\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$.
• M=Men, D=Days, H=Hours, W=Work (Output).

If A is $n$ times efficient as B.

• Eff Ratio: $A:B = n:1$.
• Time Ratio: $A:B = 1:n$ (Inverse).
• Combined: Eff $(n+1)$.

Working on turns.

• Logic: Find work done in 1 cycle (usually 2 days: A then B).
• Divide Total Work by Cycle Work. Handle remainder manually.

Money is distributed based on Work Done (not just Time).

• Rule: Wage Ratio = Efficiency $\times$ Time.
• If Time same, Wage $\propto$ Efficiency.

Same as Time & Work, but Leaks are Negative.

• Inlet: Positive Efficiency (+).
• Outlet/Leak: Negative Efficiency (-).

When someone leaves $n$ days BEFORE completion.

• Hack: Do not subtract. ADD their work.
• $Total Work + (Person \times Days)$. Divide by Total Efficiency.

For problems like '3 Men OR 5 Women'.

• Formula: $\text{Days} = \frac{\text{Given Days}}{ \frac{M_2}{M_1} + \frac{W_2}{W_1} }$.
• Faster than converting Men to Women.