Rowan plan vs. 50–50 Halsey plan For which relationship between actual time and standard time do both plans yield the same worker earnings?

Introduction / Context:Rowan and Halsey (50–50) are classic time-saved incentive plans. Comparing their earnings at different performance levels helps select a plan and set expectations for workers and management.

Given Data / Assumptions:

• Standard time = S, actual time = T, rate = R.
• Halsey 50–50 bonus = 0.5 * (S − T) * R.
• Rowan bonus = (Time saved / Standard time) * T * R = ((S − T)/S) * T * R.

Concept / Approach:We compare total earnings E under both plans and find when they are equal by substituting a specific T relative to S.

Step-by-Step Solution:Let T = S/2.Halsey 50–50: Bonus = 0.5 * (S − S/2) * R = 0.25 S R; Earnings = T R + Bonus = 0.5 S R + 0.25 S R = 0.75 S R.Rowan: Bonus = ((S − S/2)/S) * (S/2) * R = (0.5) * (0.5 S) * R = 0.25 S R; Earnings = T R + Bonus = 0.5 S R + 0.25 S R = 0.75 S R.Thus, at T = S/2, both plans give identical earnings.

Verification / Alternative check:Trying another T (e.g., T = 0.7 S) yields different bonuses, confirming equality occurs specifically at half the standard time.

Why Other Options Are Wrong:At one-fourth, equal, twice, or three-fourths of S, the two formulas do not coincide; computed bonuses differ.

Common Pitfalls:Confusing time-saved based bonuses with efficiency-based plans or forgetting the 50% share in Halsey.

Final Answer:Actual time is one-half of standard time