Topic Details (Notes format)

How to Solve Work-Rate Problems

Subject: Mathematics

Book: Maths Mastery

Work-rate problems revolve around the formula Work = Rate × Time, often focusing on collaborative tasks. For example, if Person A can complete a job in 6 hours (rate = 1/6 job/hour) and Person B can do it in 3 hours (rate = 1/3 job/hour), together their combined rate is 1/6 + 1/3 = 1/2 job/hour, so they finish in 2 hours. Work-rate logic extends to real-life scheduling—like painting rooms, manufacturing tasks, or data processing. Mastering these setups helps you optimize resource use, plan effectively, and interpret team-based productivity measurements.

Practice Questions

If a:b = 3:4 and b:c = 5:6, what is a:c?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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What is the sum of all angles in a hexagon?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If 3x = 81, what is the value of x?

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What is the HCF of 48 and 180?

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