Choose an exam and explore concepts through visual explanations, topic maps and revision checks. Open the full chapter notes whenever you need more detail.
THE VISUAL LEARNING STUDIO
See the idea. Understand the connection.
35 visual explanations across 29 chapters, with topic maps throughout the library.
The chapter index will grow as additional notes are prepared. Chapters shown here are a learning collection, not a claim that the entire exam syllabus is complete.
SEE IT. CONNECT IT. EXPLAIN IT.
Understand the chapter visually
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Study the expanded notes and the credited detailed textbook lessons. The current chapter index covers core topics; it is not a claim of exhaustive coverage of every examination syllabus. Check the official syllabus and primary references.
Time and Work — lesson overview
Rates of work
If one person completes a job in a days at a constant rate, the rate is 1/a of the job per day.
Independent simultaneous rates add when workers contribute without changing one another’s stated productivity.
Completion times do not add in the same way as rates. Define one whole job or a convenient common-unit total first.
Worked example
A completes a task in 6 days and B in 3 days. Their combined rate is 1/6+1/3=1/2 job per day.
Together they finish in two days under constant independent-rate assumptions. Averaging 6 and 3 days would not give the correct combined time.
If one process removes work, such as a leak opposing a filling pipe, its rate is subtracted with a consistent sign convention.
People and changing conditions
Worker-days are useful only when per-worker productivity and working hours are held appropriately constant.
If more workers cause coordination delays, the simple inverse-proportion model may not describe reality; follow the question’s assumptions.
For staged work, calculate the fraction completed in each stage, subtract from the whole and solve for the remaining time.
