List

Ratio, Proportion and Rates of Change - Short Problems

Race Time
problem

Race Time

Age
11 to 14
Challenge level
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Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.
Dean's Mountain
problem

Dean's Mountain

Age
11 to 14
Challenge level
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Dean runs down the mountain at 12 km per hour. How long does it take him to run down the mountain?
Placeholder: several colourful numbers
problem

Draining a pool

Age
11 to 14
Challenge level
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The water is being drained from a pool. After how long will the depth of the pool be 144 cm?
Three of a Kind
problem

Three of a Kind

Age
11 to 14
Challenge level
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How long is it between 5:55 and the next time all three digits on a digital clock are the same?
Printer Ink
problem

Printer Ink

Age
11 to 14
Challenge level
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A small ink cartridge has enough ink to print 600 pages. How many pages can be printed using a large ink cartridge?
A Classy Ratio
problem

A Classy Ratio

Age
11 to 14
Challenge level
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There are six more girls than boys in Miss Spelling's class of 24 pupils. What is the ratio of girls to boys in the class?
Athletics Club
problem

Athletics Club

Age
11 to 14
Challenge level
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An athletics club has girl, boy and adult members. How many members does the club have?
Family Fortune
problem

Family Fortune

Age
11 to 14
Challenge level
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If three brothers will get £20 more if they do not share their money with their sister, how much money is there?
Eating Beans
problem

Eating Beans

Age
11 to 14
Challenge level
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The Bean family are very particular about beans. At every meal all Beans eat some beans... At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?
24 Hour Conundrum
problem

24 Hour Conundrum

Age
11 to 14
Challenge level
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It is 225 minutes until midnight. What time is it on a 24-hour digital clock?
Flying Down Under
problem

Flying Down Under

Age
11 to 14
Challenge level
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Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?
Turbo Tortoise
problem

Turbo Tortoise

Age
11 to 14
Challenge level
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Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?
Brothers and sisters
problem

Brothers and sisters

Age
11 to 14
Challenge level
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Can you work out how many brothers and sisters are in the family?
Minutes In between
problem

Minutes In between

Age
11 to 14
Challenge level
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How many minutes are there between 11:41 and 14:02?
speed over a bridge
problem

speed over a bridge

Age
11 to 14
Challenge level
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How fast is the train travelling as it goes over the bridge?
Flapjack
problem

Flapjack

Age
11 to 14
Challenge level
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A recipe for flapjacks calls for a certain quantity of butter, sugar and oats. Given the amount of these ingredients I have, how many flapjacks can I make?
Roman Distances
problem

Roman Distances

Age
11 to 14
Challenge level
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Marcus' atrium was a square with each side 50 pedes long. How many times did Marcus have to walk round his atrium to complete his daily exercise of 8 stadia?
Thunder and Lightning
problem

Thunder and Lightning

Age
11 to 14
Challenge level
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How far away was the lightning if the flash and the thunderclap were 6 seconds apart?
Placeholder: several colourful numbers
problem

Musical Maths

Age
11 to 14
Challenge level
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Approximately how long is five hundred and twenty five thousand six hundred minutes?
Don't Be Late
problem

Don't Be Late

Age
11 to 14
Challenge level
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Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.
Placeholder: several colourful numbers
problem

Ratio Swap

Age
11 to 14
Challenge level
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How many adults would need to join this group of people to reverse this ratio?
Off the Cuff
problem

Off the Cuff

Age
11 to 14
Challenge level
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Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?
A Leg to Stand On
problem

A Leg to Stand On

Age
11 to 14
Challenge level
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Can you work out the number of chairs at a cafe from the number of legs?
Placeholder: several colourful numbers
problem

The elephant diet

Age
11 to 14
Challenge level
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Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
Out of Sync
problem

Out of Sync

Age
11 to 14
Challenge level
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Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?
Decimal Clock
problem

Decimal Clock

Age
11 to 14
Challenge level
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A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?
Sharing Sweets
problem

Sharing Sweets

Age
11 to 14
Challenge level
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Maria and Lucy spun a coin 30 times, and gave each other sweets depending on the outcome of the spin. How many times was tails spun?
How many Swimmers?
problem

How many Swimmers?

Age
11 to 14
Challenge level
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Given the ratios of junior to senior and senior to veteran members, can you work out what the smallest possible number of members in a swimming club is?
Stair Climb
problem

Stair Climb

Age
11 to 14
Challenge level
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Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?
Fruit Basket Ratio
problem

Fruit Basket Ratio

Age
11 to 14
Challenge level
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From two ratios of apples and oranges in a fruit bowl, can you work out how many fruits there are?
Tyre Wear
problem

Tyre Wear

Age
11 to 14
Challenge level
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A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?
Leg It
problem

Leg It

Age
11 to 14
Challenge level
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How far from the finishing line should these runners start to make the race 'fair'?
Placeholder: several colourful numbers
problem

Washing elephants

Age
11 to 14
Challenge level
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How long will it take Mary and Nigel to wash an elephant if they work together?
Revolutions
problem

Revolutions

Age
11 to 14
Challenge level
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Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?
Hiking the Hill
problem

Hiking the Hill

Age
14 to 16
Challenge level
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Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?
Tummy Ache
problem

Tummy Ache

Age
14 to 16
Challenge level
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Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?
The London Eye
problem

The London Eye

Age
14 to 16
Challenge level
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The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
Caught in the Web
problem

Caught in the Web

Age
14 to 16
Challenge level
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Can you estimate the mass of insects caught by spiders in the UK each year?
Honey Bees
problem

Honey Bees

Age
14 to 16
Challenge level
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How many bees could fly 1000 miles if they had 10 gallons of honey?
Walking in the Mountains
problem

Walking in the Mountains

Age
14 to 16
Challenge level
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Heidi and Peter pass two signs which say how far their destination is. How long will it take them to get there?
Shepherd's Flock
problem

Shepherd's Flock

Age
14 to 16
Challenge level
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Does Joseph have too many sheep in his flock...
Overtake
problem

Overtake

Age
14 to 16
Challenge level
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Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?
Bike Shop
problem

Bike Shop

Age
14 to 16
Challenge level
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If I walk to the bike shop, but then cycle back, what is my average speed?
Placeholder: several colourful numbers
problem

Dolly Dolphin

Age
14 to 16
Challenge level
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Can you find Dolly Dolphin's average speed as she swims with and against the current?
Travelling by Train
problem

Travelling by Train

Age
14 to 16
Challenge level
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Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?
Hillwalking
problem

Hillwalking

Age
14 to 16
Challenge level
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Andrew walks along a flat path, then up and down a hill, then back along the path. Is it possible to work out how far he has walked?
Very Long Line
problem

Very Long Line

Age
14 to 16
Challenge level
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If the line on the right were 0.2mm thick, how long would it need to be to cover an area of one square metre?
Travelator
problem

Travelator

Age
14 to 16
Challenge level
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When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
Ratio Riddle
problem

Ratio Riddle

Age
14 to 16
Challenge level
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Can you work out the ratio b:c given the ratios a:b and a:c?
Crude Calculation
problem

Crude Calculation

Age
14 to 16
Challenge level
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Louise has noticed that the price of petrol has changed. Can you work out the percentage that it has increased by?
Antifreeze
problem

Antifreeze

Age
14 to 16
Challenge level
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How much more antifreeze is needed to make the proportion 30%?
Platinum Puzzle
problem

Platinum Puzzle

Age
14 to 16
Challenge level
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What is the approximate total volume of platinum that has ever been produced?
Placeholder: several colourful numbers
problem

Pond Runners

Age
14 to 16
Challenge level
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Can you work out how much time it will be before Katherine laps James around the pond?
Placeholder: several colourful numbers
problem

Petrol Stop

Age
14 to 16
Challenge level
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From the information given, can you work out how long Roberto drove for after putting petrol in his car?
Placeholder: several colourful numbers
problem

Candles

Age
14 to 16
Challenge level
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What is the ratio of the lengths of the candles?
Televisual Technology
problem

Televisual Technology

Age
14 to 16
Challenge level
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If a new and an old television have screens of the same area, what is the ratio of their widths?
Traffic Jam
problem

Traffic Jam

Age
14 to 16
Challenge level
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Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced?
Placeholder: several colourful numbers
problem

Two trains

Age
14 to 16
Challenge level
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Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?
Marathon Mission
problem

Marathon Mission

Age
14 to 16
Challenge level
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Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?
Flower Show
problem

Flower Show

Age
14 to 16
Challenge level
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How long will it take six gardeners to dig six circular flower beds?
Late for work
problem

Late for work

Age
14 to 16
Challenge level
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What average speed should Ms Fanthorpe drive at to arrive at work on time?
Placeholder: several colourful numbers
problem

Walk Up the Escalator

Age
14 to 16
Challenge level
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Can you work out how long Aimee would take to get up the escalator if she walked?
Placeholder: several colourful numbers
problem

100m sprint

Age
14 to 16
Challenge level
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Anna, Bridget and Carol run a race. Can you work out where Carol was when Anna finished?
Placeholder: several colourful numbers
problem

Day Out

Age
14 to 16
Challenge level
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Chris cycled faster than expected. Can you work out his average speed?
Boys and Girls
problem

Boys and Girls

Age
14 to 16
Challenge level
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Can you find the total number of students in the school, given some information about ratios?
Placeholder: several colourful numbers
problem

Laps

Age
14 to 16
Challenge level
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On which of the hare's laps will she first pass the tortoise?
Backwards laps
problem

Backwards laps

Age
14 to 16
Challenge level
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If two friends run in opposite directions around a track, and they pass each other every 24 seconds, how long do they take to complete a lap?