Unitary method application on constant-rate production: A worker makes one toy every 2 hours at a steady, uniform rate. If he continues working at the same speed for a total of 80 hours, how many complete toys will he manufacture in that period?

Introduction / Context:This problem is a classic unitary-method question involving constant-rate production. We are told how long it takes to produce one unit (a toy) and asked to scale that rate to a longer total time, assuming the worker continues at the same steady pace without interruptions or speed changes.

Given Data / Assumptions:

• Production time per toy = 2 hours per toy
• Total available working time = 80 hours
• Rate is constant; partial toys are not counted because the question asks for complete toys produced.

Concept / Approach:When the rate is given as time per unit, the number of units completed is total time divided by time per unit. This is the unitary method: first compute how many toys per hour (or invert time-per-toy), then scale to the full duration.

Step-by-Step Solution:Time per toy = 2 hTotal time available = 80 hNumber of toys = total time / time per toyNumber of toys = 80 / 2 = 40

Verification / Alternative check:Alternatively, compute the rate as 0.5 toy per hour. Over 80 hours, 0.5 * 80 = 40 toys, confirming the same result.

Why Other Options Are Wrong:54 and 45 imply faster production than stated; 39 implies a slower rate; 42 is another distractor not consistent with 2 hours per toy over 80 hours.

Common Pitfalls:Confusing 2 hours per toy with 2 toys per hour (the latter would give 160 toys, which is wrong). Always take care when inverting units and interpreting “per”.

Final Answer:40