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

A train 150 m long passes a pole in 15 seconds. What is its speed?

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

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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

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How many ways can 4 people sit in a row?

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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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If sin(A) = 1/2 and A is acute, what is the value of A?

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What is the cube of 4?

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The LCM of 12 and 15 is:

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