Key Takeaways
In this article I will cover:
- Learn the Formula Triangle: Every question gives you two of speed, distance and time and asks for the third. The triangle tells you which calculation to run, every time.
- Memorise Key Conversions: Most questions that look hard are only hard in the wrong units. A handful of memorised conversions turns them into times tables.
- Speed Is Paramount: Aim for 10 to 15 seconds a calculation. A single plan can call for dozens, and the time you save is time you keep for the plan itself.
- Performing Under Pressure: The DS will make you calculate out loud in your brief. Drill until the method is automatic, then practise saying the working aloud.
- Double Jeopardy: The same skill is tested again in the numerical reasoning test at both Briefing and Main Board, so the drilling earns its keep twice over.
I still vividly remember my mind going blank. For what felt like an eternity, I stood there in silence. "Mr Moffat. I'll ask you again. What time will you arrive at the hospital?" The DS were waiting for an answer, and they weren't being patient about it. Until then, my mental maths had been solid, if not spectacular. My plan wasn't perfect, but I knew it worked and the timings were sound. None of that mattered if I couldn't adapt when the pressure was on.
I had just been asked a simple speed, distance, time question at the end of my planning exercise brief, and I had frozen. This was not good. Luckily, just in time, my brain snapped back into gear. "12:30, ma'am." "Are you sure?" "Yes, ma'am." I hadn't exactly covered myself in glory, but I had narrowly averted disaster. The hours I had spent drilling speed, distance and time calculations had just about paid off.
That moment is why this guide exists. Below are the tricks and tips that can give you an edge when it comes to speed, distance and time calculations. They include the formula triangle, the conversions worth memorising, the methods that turn awkward numbers into clean ones, and the drilling that makes it all hold up when it counts.
Where Speed, Distance & Time Appears at AOSB
Speed, distance and time questions turn up in two places at AOSB. Firstly, and most significantly, you will rely on them constantly during the planning exercise. Secondly, you will need them in the numerical reasoning test.
The planning exercise is where they matter most. A single plan can call for dozens of calculations, and every timing in your plan depends on getting them right. Then, in the brief, the DS will fire fresh ones at you on the spot, exactly as happened to me.
The numerical reasoning test is the second place. Speed, distance and time is one of its fifteen question types, and the test is sat at both Briefing and Main Board with no calculator. That is why the drilling pays twice.
The Formula Triangle
The formula triangle is a single diagram that replaces the three speed, distance and time formulas. Every question gives you two of the three quantities and asks for the third, and the triangle tells you which calculation gets you there.
D ÷ T
Speed = Distance ÷ Time
S × T
Distance = Speed × Time
D ÷ S
Time = Distance ÷ Speed
To read it, cover the quantity you are looking for and perform the calculation left in the other two cells. Cover the S and you are left with D over T, so divide distance by time. Cover the D and you are left with S beside T, so multiply speed by time.
Learn the layout once and you never have to remember which way round a calculation goes. The triangle tells you every time.
The Conversions to Memorise
These conversions turn a hard-looking calculation into one you already know. Learn each one by heart, in both directions, so under pressure you can recall them at speed rather than derive them.
Fraction Clock
| Minutes | Of an hour |
|---|---|
| 5 | 1/12 |
| 6 | 1/10 |
| 10 | 1/6 |
| 12 | 1/5 |
| 15 | 1/4 |
| 20 | 1/3 |
| 25 | 5/12 |
| 30 | 1/2 |
| 35 | 7/12 |
| 40 | 2/3 |
| 45 | 3/4 |
| 50 | 5/6 |
| 55 | 11/12 |
Slow Speeds
| Speed | Mins per km |
|---|---|
| 60 kph | 1 |
| 30 kph | 2 |
| 24 kph | 2.5 |
| 20 kph | 3 |
| 15 kph | 4 |
| 12 kph | 5 |
| 10 kph | 6 |
| 6 kph | 10 |
| 5 kph | 12 |
| 4 kph | 15 |
| 3 kph | 20 |
| 2 kph | 30 |
| 1 kph | 60 |
Fast Speeds
| Speed | Km per min |
|---|---|
| 60 kph | 1 |
| 120 kph | 2 |
| 180 kph | 3 |
| 240 kph | 4 |
| 300 kph | 5 |
| 360 kph | 6 |
| 420 kph | 7 |
| 480 kph | 8 |
| 540 kph | 9 |
| 600 kph | 10 |
| 660 kph | 11 |
| 720 kph | 12 |
| 780 kph | 13 |
The slow speeds table earns its place in the planning exercise, where boats, tractors and men on foot rarely move at a convenient 60 kph. Knowing that 4 kph means 15 minutes per kilometre turns a march timing into a times table.
Methods for Awkward Numbers
Most questions that look hard are only hard in the wrong units. Decide whether to work in hours or in minutes before you calculate, and pick whichever makes the numbers clean. If the numbers feel awkward, you have probably picked the wrong mode, so switch and try again.
Split the Time
When the time is hours and minutes together, deal with the whole hours first. Then take the leftover minutes as a fraction of an hour, and add the two parts.
At 65 kph, how far do you travel in 5 hours and 12 minutes?
Take the whole hours, then the 12 minutes as a fifth of an hour, and add the two parts.
Double to Clear the Half Hour
Speed is a ratio, so doubling distance and time together leaves it unchanged. When a time ends in 30 minutes, double both numbers and the half hour becomes a whole one.
What speed covers 385 km in 3 hours and 30 minutes?
Double the distance and the time together so the half hour becomes a whole hour, then divide.
Break Numbers Into Easy Chunks
When a multiplication looks too big, split one number into pieces you know, multiply each piece, and add. Tens and units is usually the right split.
Take 44 kph for 2 hours and 15 minutes. The whole hours give 88 km, the quarter hour gives 11 km, and together that is 99 km without a single hard sum.
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Performing Under Pressure
Being able to do these calculations at your desk is not the only skill AOSB is testing. The skill is doing them mid-brief, with the DS waiting on your answer and your plan on the line.
There is no shortcut here. The methods above only hold up under pressure once they are automatic, and automatic means drilled.
Practise out loud as well as on paper. In the brief you will be talking the DS through your timings rather than working in silence, and saying the working aloud is a different skill from thinking it.
Try the four below. Do the first three in your head, then say the last one out loud in full sentences, as if the DS has just asked you for it.
A convoy travels at 48 kph for 45 minutes. How far does it travel?
A patrol marches 5 km at 4 kph. How long does it take?
A truck travels at 55 kph for 2 hours and 12 minutes. How far does it go?
What speed covers 210 km in 3 hours and 30 minutes?
These are the same style of drills as the Mental Maths tests inside Officer Ready. Twenty questions against the clock, with every answer explained and a detailed breakdown on how you do on each of the three calculation types.
Speed, Distance & Time in the Plan Ex
In the planning exercise, speed, distance and time questions don't arrive as neat one-liners. They arrive buried in a scenario.
That is a different level of difficulty from single drills, as it adds complexity. The calculation is rarely the hard part. The hard part is holding the moving pieces in your head while you do it.
Below is one of the map scenarios from the Officer Ready Mental Maths module, and it is one of the harder ones. Read the brief, study the map, then try the question before revealing the answer.
Scenario Brief & Speeds
You run the rescue base at the foot of Glen Reva Mountain. A walker is hurt at Mara Hut, high at the glen head, and must reach Glen Base before last light at 1930.
The Land Rover keeps to the glen road and stops at the Track Head. The argocat can take the rough upper track to Coll Hut. Above here, the ground is too steep for vehicles, so the last climb is on foot. Sorn Pass takes 30 minutes to cross.
| Land Rover on the glen road | 30 kph |
| Argocat on the upper track | 12 kph |
| On foot | 5 kph |
A medic must reach the casualty at Mara Hut before last light at 1930. The medic drives the Land Rover up the glen road to the Track Head, rides the argocat on to Coll Hut, then climbs the last stretch to Mara Hut on foot. What is the latest time the medic can leave Glen Base?
The full module has six of these scenarios, each sat against the clock, alongside the drill tests. Together they take you from the triangle to brief-ready.
Frequently Asked Questions
Can you use a calculator in the planning exercise at AOSB?
No. Every timing in your plan and every question in the brief must be worked out in your head, and the same is true of the numerical reasoning test. That is why memorised conversions and a drilled method matter more than raw maths ability.
How fast should my speed, distance and time calculations be?
Aim for 10 to 15 seconds a calculation once you have found the clean route. If a question is taking you longer than 30 seconds, you have almost always missed a conversion rather than run out of ability.
What conversions should I memorise for speed, distance and time questions?
Learn the minutes-to-fractions-of-an-hour clock, the minutes-per-kilometre figures for slow speeds, and the kilometres-per-minute figures for fast speeds. Learn each one in both directions until recall is instant.
Do speed, distance and time questions appear in the numerical reasoning test?
Yes. Speed, distance and time is one of the fifteen question types in the numerical reasoning test, which is sat at both Briefing and Main Board without a calculator. The techniques in this guide transfer directly.
How do I practise speed, distance and time for the planning exercise?
Drill single calculations against the clock until they are automatic, then move to full scenarios where you choose routes and count back from deadlines. Practise saying your working out loud, because the brief tests spoken maths, not silent maths.
Final Thoughts
I never found out whether the DS knew how close I came to unravelling. What I do know is that the answer arrived because the drilling had put it somewhere the pressure could not reach.
That is the whole game with speed, distance and time. Learn the triangle, memorise the conversions, then drill until the mental maths is one thing you don't have to worry about when you get to Westbury.
Ready to Begin Your Prep?
The Officer Ready Mental Maths modules drill speed, distance and time exactly as the planning exercise demands. Timed drills, map scenarios, and every answer explained.
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