AQA · Mathematics · 8300
GCSE Maths: Proportion: Time
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Proportion: Time (Corbettmaths Video 255), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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If 5 people take 40 minutes to dig a vegetable patch, how long would it take 1 person?
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200 minutes. With inverse proportion, 1 person takes 5 times as long: 5 × 40 = 200.
If 5 people take 40 minutes to dig a vegetable patch, how long would it take 8 people?
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25 minutes. Total work = 5 × 40 = 200 person-minutes. Divide by 8 people: 200 ÷ 8 = 25.
What assumption is typically made when solving inverse proportion problems with workers?
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All workers work at the same constant rate throughout the task.
If it takes 48 minutes to empty a pool using 4 pumps, how long would it take using 3 pumps?
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64 minutes. Total work = 4 × 48 = 192 pump-minutes. Divide by 3 pumps: 192 ÷ 3 = 64.
If Harold decorates 36 cupcakes in 15 minutes at a constant rate, how long does he take per cupcake?
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25 seconds per cupcake. 15 minutes = 900 seconds. 900 ÷ 36 = 25 seconds.
If 8 machines take 40 hours to make a number of pencils, how long would 10 machines take?
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32 hours. Total work = 8 × 40 = 320 machine-hours. Divide by 10 machines: 320 ÷ 10 = 32.
A printer prints 3000 black and white pages per hour. How many pages can it print in 2.5 hours?
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7500 pages. 3000 × 2.5 = 7500.
If 12 waiters can serve food to all guests in 16 minutes, how many waiters are needed to serve in less than 10 minutes?
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At least 20 waiters. Total work = 12 × 16 = 192 waiter-minutes. For under 10 minutes: 192 ÷ 10 = 19.2, so need 20 waiters.
If 20 workers take 15 hours to seed 40 acres, how long would 10 workers take to seed 90 acres?
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67.5 hours. Rate = 40 acres ÷ (20 × 15) = 0.133... acres per worker-hour. For 90 acres with 10 workers: 90 ÷ (10 × 0.133...) = 67.5 hours.
If 5 builders can build a house in 24 days working 10 hours per day, how many days for 4 builders working 6 hours per day?
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50 days. Total work = 5 × 24 × 10 = 1200 builder-hours. For 4 builders at 6 hours/day: 1200 ÷ (4 × 6) = 50 days.
In inverse proportion problems with time and workers, what happens to time when the number of workers increases?
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Time decreases. More workers complete the same task in less time (assuming constant work rate per worker).
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