# Ratio, Proportion and Rates of Change - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Ratio, Proportion and Rates of Change.

Printable worksheets containing selections of these problems are available here.

### Roman Distances

##### Age 11 to 14 ShortChallenge Level

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

##### Age 11 to 14 ShortChallenge Level

How far away was the lightning if the flash and the thunderclap were 6 seconds apart?

### Three of a Kind

##### Age 11 to 14 ShortChallenge Level

How long is it between 5:55 and the next time all three digits on a digital clock are the same?

### Printer Ink

##### Age 11 to 14 ShortChallenge Level

A small ink cartridge has enough ink to print 600 pages. How many pages can be printed using a large ink cartridge?

### Flying Down Under

##### Age 11 to 14 ShortChallenge Level

Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?

### A Classy Ratio

##### Age 11 to 14 ShortChallenge Level

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?

### Turbo Tortoise

##### Age 11 to 14 ShortChallenge Level

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

##### Age 11 to 14 ShortChallenge Level

Can you work out how many brothers and sisters are in the family?

### Dean's Mountain

##### Age 11 to 14 ShortChallenge Level

Dean runs down the mountain at 12 km per hour. How long does it take him to run down the mountain?

### Draining a Pool

##### Age 11 to 14 ShortChallenge Level

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

### Race Time

##### Age 11 to 14 ShortChallenge Level

Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

### Athletics Club

##### Age 11 to 14 ShortChallenge Level

An athletics club has girl, boy and adult members. How many members does the club have?

### Minutes in Between

##### Age 11 to 14 ShortChallenge Level

How many minutes are there between 11:41 and 14:02?

### Speed over a Bridge

##### Age 11 to 14 ShortChallenge Level

How fast is the train travelling as it goes over the bridge?

### Family Fortune

##### Age 11 to 14 ShortChallenge Level

If three brothers will get Â£20 more if they do not share their money with their sister, how much money is there?

### Flapjack

##### Age 11 to 14 ShortChallenge Level

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?

### Eating Beans

##### Age 11 to 14 ShortChallenge Level

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

##### Age 11 to 14 ShortChallenge Level

It is 225 minutes until midnight. What time is it on a 24-hour digital clock?

### Sharing Sweets

##### Age 11 to 14 ShortChallenge Level

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?

### Tyre Wear

##### Age 11 to 14 ShortChallenge Level

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?

### A Leg to Stand On

##### Age 11 to 14 ShortChallenge Level

Can you work out the number of chairs at a cafe from the number of legs?

### Fruit Basket Ratio

##### Age 11 to 14 ShortChallenge Level

From two ratios of apples and oranges in a fruit bowl, can you work out how many fruits there are?

### How Many Swimmers?

##### Age 11 to 14 ShortChallenge Level

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?

### Leg It

##### Age 11 to 14 ShortChallenge Level

How far from the finishing line should these runners start to make the race 'fair'?

### Out of Sync

##### Age 11 to 14 ShortChallenge Level

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

### Stair Climb

##### Age 11 to 14 ShortChallenge Level

Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?

### Decimal Clock

##### Age 11 to 14 ShortChallenge Level

A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?

### Off the Cuff

##### Age 11 to 14 ShortChallenge Level

Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

### Musical Maths

##### Age 11 to 14 ShortChallenge Level

Approximately how long is five hundred and twenty five thousand six hundred minutes?

### The Elephant Diet

##### Age 11 to 14 ShortChallenge Level

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

### Don't Be Late

##### Age 11 to 14 ShortChallenge Level

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

### Ratio Swap

##### Age 11 to 14 ShortChallenge Level

How many adults would need to join this group of people to reverse this ratio?

### Revolutions

##### Age 11 to 14 ShortChallenge Level

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

### Washing Elephants

##### Age 11 to 14 ShortChallenge Level

How long will it take Mary and Nigel to wash an elephant if they work together?

### Honey Bees

##### Age 14 to 16 ShortChallenge Level

How many bees could fly 1000 miles if they had 10 gallons of honey?

### Tummy Ache

##### Age 14 to 16 ShortChallenge Level

Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?

### Hiking the Hill

##### Age 14 to 16 ShortChallenge Level

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?

### The London Eye

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

Can you estimate the mass of insects caught by spiders in the UK each year?

### Ratio Riddle

##### Age 14 to 16 ShortChallenge Level

Can you work out the ratio b:c given the ratios a:b and a:c?

### Very Long Line

##### Age 14 to 16 ShortChallenge Level

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?

### Overtake

##### Age 14 to 16 ShortChallenge Level

Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

### Tyneside Average Speed

##### Age 14 to 16 ShortChallenge Level

Can you work out the average speed of the van?

### Platinum Puzzle

##### Age 14 to 16 ShortChallenge Level

What is the approximate total volume of platinum that has ever been produced?

### Pond Runners

##### Age 14 to 16 ShortChallenge Level

Can you work out how much time it will be before Katherine laps James around the pond?

### Dolly Dolphin

##### Age 14 to 16 ShortChallenge Level

Can you find Dolly Dolphin's average speed as she swims with and against the current?

### Bike Shop

##### Age 14 to 16 ShortChallenge Level

If I walk to the bike shop, but then cycle back, what is my average speed?

### Crude Calculation

##### Age 14 to 16 ShortChallenge Level

Louise has noticed that the price of petrol has changed. Can you work out the percentage that it has increased by?

### Walking in the Mountains

##### Age 14 to 16 ShortChallenge Level

Heidi and Peter pass two signs which say how far their destination is. How long will it take them to get there?

### Antifreeze

##### Age 14 to 16 ShortChallenge Level

How much more antifreeze is needed to make the proportion 30%?

### Inches and Barleycorns

##### Age 14 to 16 ShortChallenge Level

How many barleycorns are there in one inch?

### Travelling by Train

##### Age 14 to 16 ShortChallenge Level

Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?

### Shepherd's Flock

##### Age 14 to 16 ShortChallenge Level

Does Joseph have too many sheep in his flock...

### Travelator

##### Age 14 to 16 ShortChallenge Level

When Andrew arrives at the end of the walkway, how far is he ahead of Bill?

### Hillwalking

##### Age 14 to 16 ShortChallenge Level

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?

### Laps

##### Age 14 to 16 ShortChallenge Level

On which of the hare's laps will she first pass the tortoise?

### Two Trains

##### Age 14 to 16 ShortChallenge Level

Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?

### Fraction of Percentages

##### Age 14 to 16 ShortChallenge Level

What is $W$ as a fraction of $Z?$

### Traffic Jam

##### Age 14 to 16 ShortChallenge Level

Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced?

### Late for Work

##### Age 14 to 16 ShortChallenge Level

What average speed should Ms Fanthorpe drive at to arrive at work on time?

### Backwards Laps

##### Age 14 to 16 ShortChallenge Level

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?

### Day Out

##### Age 14 to 16 ShortChallenge Level

Chris cycled faster than expected. Can you work out his average speed?

### Candles

##### Age 14 to 16 ShortChallenge Level

What is the ratio of the lengths of the candles?

### Petrol Stop

##### Age 14 to 16 ShortChallenge Level

From the information given, can you work out how long Roberto drove for after putting petrol in his car?

### Marathon Mission

##### Age 14 to 16 ShortChallenge Level

Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?

### Walk up the Escalator

##### Age 14 to 16 ShortChallenge Level

Can you work out how long Aimee would take to get up the escalator if she walked?

### 100m Sprint

##### Age 14 to 16 ShortChallenge Level

Anna, Bridget and Carol run a race. Can you work out where Carol was when Anna finished?

### Flower Show

##### Age 14 to 16 ShortChallenge Level

How long will it take six gardeners to dig six circular flower beds?

### Boys and Girls

##### Age 14 to 16 ShortChallenge Level

Can you find the total number of students in the school, given some information about ratios?

### Televisual Technology

##### Age 14 to 16 ShortChallenge Level

If a new and an old television have screens of the same area, what is the ratio of their widths?