# Units of Measurement - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Units of Measurement.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions Stage 4 ★★ Sheet 1 Solutions

### Roman Distances

##### KS 3 Short Challenge Level:

Weekly Problem 9 - 2009
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?

### Hiking the Hill

##### KS 3 Short Challenge Level:

Weekly Problem 22 - 2011
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?

### Millenium Leap

##### KS 3 Short Challenge Level:

Weekly Problem 18 - 2012
How many leap years will there be between 2001 and 3001?

### Thunder and Lightning

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2009
How far away was the lightning if the flash and the thunderclap were 6 seconds apart?

### Caught in the Web

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2012
Can you estimate the mass of insects caught by spiders in the UK each year?

### Overbearing

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2009
In a village the pub, church and school are at different lengths and bearings from each other. What is the bearing of the school from the church?

### Flying Down Under

##### KS 3 Short Challenge Level:

Weekly Problem 53 - 2009
Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?

### Dean's Mountain

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2016
Dean runs up a mountain road at 8 km per hour. It takes him one hour to get to the top. He runs down the same mountain at 12 km per hour. How long does it take him to run down the mountain?

### Three of a Kind

##### KS 3 Short Challenge Level:

Weekly Problem 16 - 2013
How long is it between 5:55 and the next time all three digits on a digital clock are the same?

### Walking in the Mountains

##### KS 3 Short Challenge Level:

Weekly Problem 5 - 2010
Heidi and Peter are walking through the mountains. They pass two signs which say how far away their destination is, so can you work out how long it will take them to get there?

### Wiggly Conversions

##### KS 3 Short Challenge Level:

Weekly Problem 42 - 2011
Four wiggles equal three woggles. Two woggles equal five waggles. Six waggles equal one wuggle. Using these, can you work out which of four values is the smallest?

### Speed over a Bridge

##### KS 3 Short Challenge Level:

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

### Turbo Tortoise

##### KS 3 Short Challenge Level:

Weekly Problem 40 - 2007
Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?

### Travelling by Train

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2016
Stephen leaves Middlesborough by train at 09:00. The train travels the first 27km at 96km/h. It then stops at Darlington for 3 minutes, before travelling the remaining 29km to Durham at 96km/h. At what time does Stephen arrive at Durham?

### Race Time!

##### KS 3 Short Challenge Level:

Weekly Problem 9 - 2010
Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

### Sense of Direction

##### KS 3 Short Challenge Level:

Weekly Problem 5 - 2012
Can you work out the direction of Abbots Morton from Wyre Piddle?

### Minutes Inbetween

##### KS 3 Short Challenge Level:

Weekly Problem 30 - 2008
How many minutes are there between 11:41 and 14:02?

### Tummy Ache

##### KS 3 Short Challenge Level:

Weekly Problem 6 - 2012
Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?

### Measured Upside Down

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2008
Baby can't stand up yet, so we measure her upside down. Can you use our measurements to work out how much Baby has grown in her first year?

### Stair Climb

##### KS 3 Short Challenge Level:

Weekly Problem 16 - 2006
Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?

### Overtake

##### KS 3 Short Challenge Level:

Weekly Problem 19 - 2011
Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

### Bike Shop

##### KS 3 Short Challenge Level:

Weekly Problem 8 - 2013
If I walk to the bike shop, but then cycle back, what is my average speed?

### Inches and Barleycorns

##### KS 3 Short Challenge Level:

How many barleycorns are there in one inch?

### Decimal Clock

##### KS 3 Short Challenge Level:

Weekly Problem 51 - 2013
A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?

### Leg It

##### KS 3 Short Challenge Level:

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

### Don't Be Late

##### KS 3 Short Challenge Level:

Weekly Problem 31 - 2010
Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

### Very Long Line

##### KS 3 Short Challenge Level:

Weekly Problem 46 - 2016
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?

### Revolutions

##### KS 3 Short Challenge Level:

Weekly Problem 30 - 2006
Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

### The London Eye

##### KS 4 Short Challenge Level:

Weekly Problem 18 - 2014
The 80 spokes of the giant wheel The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

### Tyneside Average Speed

##### KS 4 Short Challenge Level:

Weekly Problem 12 - 2006
A van travels from Newcastle to South Shields at 30mph and returns at 40mph. What is its average speed?

### Traffic Jam

##### KS 4 Short Challenge Level:

Weekly Problem 1 - 2017
Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?

### Travelator

##### KS 4 Short Challenge Level:

Weekly Problem 25 - 2017
At the airport, the walkway moves with a speed of 4km/h and is 500m long. If Andrew walks with a speed of 6km/h and Bill stands still, how much ahead of Bill is Andrew when he finishes?

### Platinum Puzzle

##### KS 4 Short Challenge Level:

Weekly Problem 29 - 2007
What is the approximate total volume of platinum that has ever been produced?

### Hillwalking

##### KS 4 Short Challenge Level:

Weekly Problem 40 - 2016
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?

### Backwards Laps

##### KS 4 Short Challenge 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?

### Late for Work

##### KS 4 Short Challenge Level:

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