Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Rate — unit rates, combined rates and proportion-based speed problems — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Rate in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Rate revision-guide angle, while Tutopiya’s Rate subtopic page owns the learning resource and the free Rate quiz owns the practice.

Rate questions in Cambridge IGCSE Mathematics (0580/0607) test how quickly a quantity changes per unit — litres per minute, jobs per hour, cost per kilogram. They overlap with ratio and proportion but add the time dimension. Examiners often disguise rate problems inside word questions about pipes filling tanks or workers completing tasks. This guide explains what Rate covers, how to set up and solve the question types that actually appear, and where to practise.

Key takeaways

• Rate = amount ÷ time (or amount per one unit of another quantity).
• Combined rates add when workers or pipes work together in the same direction.
• Unit rate questions ask you to find “per one” — cost per item, speed per hour.
• Rate connects to Ratios and Proportions and Speed, Distance and Time.

What is Rate in Cambridge IGCSE Maths?

Rate measures how one quantity changes relative to another — usually per unit of time. Speed is the most familiar rate (distance per hour), but IGCSE also tests work rates (tasks per day) and flow rates (litres per minute). In Cambridge IGCSE Mathematics, you calculate unit rates, combine rates when processes run together, and solve inverse problems where you find time or quantity. The algebra is light; the challenge is translating words into a rate equation.

Read the full explanation, worked examples and notes on Tutopiya’s Rate subtopic page before you attempt questions.

The core ideas you must master

Idea	Formula / rule	Exam signal
Unit rate	Rate = total amount ÷ time	”per hour”, “per minute”, “per kg”
Combined rate (same job)	R_total = R₁ + R₂ + …	“working together”, “both pipes open”
Time to complete	Time = 1 ÷ rate (for one whole job)	“how long to fill the tank”
Proportion link	Rate × time = amount	”at a constant rate”

How to solve rate problems — step by step

1. Define the rate — what is changing per what? (litres per minute, pages per hour).
2. Write each worker/pipe rate as a fraction of the whole job per time unit. Pipe A fills tank in 4 h → rate = ¼ tank/hour.
3. Combine rates if they work together: add individual rates.
4. Find time or amount using rate × time = amount (or time = amount ÷ rate).
5. Check units — convert minutes to hours if rates use different time units.

Test yourself with the free Rate quiz once the setup feels natural.

Rate vs speed: when to use which subtopic

Question type	Primary subtopic	Key formula
Pipes, workers, printing pages	Rate	Combined rates add
Cars, trains, journeys	Speed, Distance and Time	D = S × T
Cost per item, density	Unit rate / proportion	Amount ÷ units

Rate in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Work out the rate	Find amount per unit time	”Work out the rate of flow in litres per minute.”
Calculate how long	Time = job ÷ combined rate	”Calculate how long both pipes take to fill the tank.”
At a constant rate	Use proportion: amount ∝ time	”At this rate, how many litres in 45 minutes?”
Show that	Prove time or amount with method	”Show that the tank is full in 2 hours 24 minutes.”
Write your answer in hours and minutes	Convert decimal hours	Common follow-up on pipe problems

Worked exam-style stems (how to answer the wording)

1. “Pipe A fills a tank in 5 hours. Pipe B fills the same tank in 10 hours. How long do both pipes take together?” Rate A = ⅕, Rate B = 1/10. Combined = ⅕ + 1/10 = 3/10 tank per hour. Time = 1 ÷ 3/10 = 10/3 hours = 3 h 20 min. Reward: reciprocal setup, correct addition of fractions.
2. “A machine prints 240 pages in 8 minutes. Work out how many pages it prints in 25 minutes at the same rate.” Unit rate = 240 ÷ 8 = 30 pages/min. In 25 min: 30 × 25 = 750 pages. Reward: unit rate first, then scaling.
3. “It costs $4.50 to buy 6 oranges. Work out the cost of 20 oranges at the same rate.” Unit cost = 4.50 ÷ 6 = $0.75 each. 20 × 0.75 = $15. Reward: per-one cost before multiplying.

Work the full set on the Number topical past-paper questions and the Rate quiz to lock the method in.

How Rate connects to the rest of Number

Proportion skills from Ratios and Proportions underpin every rate question. Journey problems often belong in Speed, Distance and Time. Use the Cambridge IGCSE Maths resource hub to move between related subtopics.

Common mistakes students make

• Adding times instead of adding rates when pipes work together (5 h and 10 h does not mean 15 h together).
• Forgetting to convert minutes and hours to the same unit before combining rates.
• Using the wrong whole — rate should be “fraction of job per hour”, not “hours per job” in the addition step.
• Confusing unit rate with total amount in proportion questions.

When you need more support

If pipe or work-rate questions keep going wrong, work through the Ratios and Proportions quiz and the Number topical past-paper questions, then get focused help from a Cambridge IGCSE Maths tutor.

Frequently asked questions

Is Rate the same as speed? Speed is a type of rate (distance per time). The Rate subtopic focuses on work and flow problems; journey questions usually sit under Speed, Distance and Time.

Why do we add rates when pipes work together? Each pipe contributes part of the tank per hour. Together they fill (fraction A + fraction B) of the tank each hour.

How do I revise Rate effectively? Practise writing “job per hour” for each worker or pipe, combine rates, then take the Rate quiz. Revisit any questions where you added times instead of rates.

Can rate questions appear on Paper 1? Yes — many are solvable without a calculator using fractions. Extended papers may use less tidy numbers.

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