Unit 11 · Algebraic / Equation Reasoning
Zara's Fence Painting — Work Rate Problem
Lesson 2 of 4
Algebraic reasoning on Selective often means turning words into a short chain of numbers — no formal algebra symbols required.
Combined-work-rate questions appear in the harder band of Selective TS but follow a fixed recipe: convert times to “fraction of job per hour,” add, then invert.
The examiner checks whether you can combine individual rates correctly (1/time each) rather than averaging the two times or adding hours naively.
Two people (or machines) complete the same job alone in different times. You find how long they take working together at constant rate.
Best approach: Rates: Zara = 1/4 job per hour, Ethan = 1/6. Together = 1/4 + 1/6. Time = 1 ÷ combined rate. Keep fractions tidy with a common denominator.
Question
Zara can paint a fence in 4 hours. Her brother Ethan can paint the same fence in 6 hours. How long will it take them to paint the fence together?
Select an answer to see the explanation.
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