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 x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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What is the value of x if log(x) + log(4) = log(32)?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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What is the length of the diagonal of a square with a side length of 7 cm?

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If the sum of three consecutive integers is 96, what are the integers?

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What is the sum of all odd numbers from 1 to 99?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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