CMA Foundation · Fundamentals of Business Mathematics and Statistics

Time and Distance for CMA Foundation Paper 3

Time and Distance is the study of how speed, distance and time relate through one rule: distance = speed × time. To solve a question, convert all units to match, pick the right speed (relative, upstream or downstream), then apply the rule. Most MCQs finish in under a minute with the right formula.

What this chapter covers

This chapter is built on one relation: distance = speed × time. Every topic is a variation of it. Speed is how fast you move, distance is how far, and time is how long. If you know any two, you can find the third.

The chapter then adds situations. Two bodies moving together or against each other need relative speed. Trains add their own length to the distance. Boats add the speed of the stream. Races and circular tracks add the idea of meeting points and head starts.

This chapter links closely to ratios and proportion, percentages, and time and work in the Business Mathematics section of Paper 3. The same inverse-proportion thinking works here: at a fixed distance, speed and time are inversely related. Practising it here makes those other chapters faster too.

Time and Distance questions are short, formula-driven and have clean numerical answers, which suits a one-hour paper of 50 MCQs with no negative marking. Once you know the handful of patterns, you can solve most questions in 30 to 60 seconds and save time for harder papers in the same session. Since Paper 3 is cleared only with at least 40% in the paper and 50% in aggregate, reliable marks from a pattern-based chapter like this are worth the effort. It is also a chapter where steady practice gives quick, visible improvement.

Time and Distance: topics in the order to study them

1Speed, Distance and Time BasicsEverything else uses distance = speed × time, unit conversion and average speed, so you must be fluent here first.
2Relative Speed and Moving BodiesSame-direction and opposite-direction speeds are the core idea that trains, boats and races all reuse.
3Problems on TrainsTrains apply relative speed directly, with the extra step of adding lengths to the distance.
4Boats and StreamsUpstream and downstream speeds follow the same add-or-subtract logic as relative speed, so it comes after you are comfortable with that.
5Races, Circular Tracks and Clocks-Style ProblemsThese combine relative speed with meeting points and head starts, so they are best left for last.

How to prepare Time and Distance

Aim to recognise the pattern in a few seconds, then apply a short formula. Build this in stages.

Learn distance = speed × time and its two rearrangements: speed = distance ÷ time and time = distance ÷ speed.
Memorise the conversion: to change km/h to m/s multiply by 5/18, and to change m/s to km/h multiply by 18/5.
Learn average speed for equal distances: 2xy ÷ (x + y). Remember it is not the simple average of two speeds.
Practise relative speed: add speeds when bodies move in opposite directions, subtract when they move in the same direction.
Solve train questions by writing the total distance to be covered first (sum of lengths, or one length for a pole or person).
For boats, write downstream = u + v and upstream = u − v, where u is boat speed in still water and v is stream speed. Then find u = (D + U) ÷ 2 and v = (D − U) ÷ 2.
Finish with timed sets of 10 mixed MCQs. Use option checking: plug an option back in if the formula is slow.

Common mistakes in Time and Distance

Averaging two speeds by simple addition and halving when the distances are equal.
Fix: Use total distance ÷ total time, or 2xy ÷ (x + y) for equal distances.
Mixing km/h with metres or seconds.
Fix: Convert everything to one unit system first, using 5/18 for km/h to m/s.
Using the wrong sign for relative speed.
Fix: Sketch the two bodies. Opposite directions add; same direction subtract.
Forgetting to add the train's length when it crosses a platform or another train.
Fix: Write the total distance first: train length plus platform or second train length.
Treating stream speed as the boat's speed in boat problems.
Fix: Label u and v clearly, then write downstream and upstream speeds before any calculation.
Ignoring options and doing long calculations.
Fix: With four options and no negative marking, test options or estimate to eliminate, and always attempt every question.

Last-day revision: Time and Distance

Distance = speed × time.
km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.
At constant distance, speed and time are inversely proportional.
Average speed = total distance ÷ total time.
For equal distances at speeds x and y, average speed = 2xy ÷ (x + y).
Opposite directions: relative speed = sum of speeds. Same direction: difference.
A train crossing a pole or a person covers its own length.
A train crossing a platform or another train covers the sum of the lengths.
Downstream speed = u + v. Upstream speed = u − v.
Still-water speed = (downstream + upstream) ÷ 2. Stream speed = (downstream − upstream) ÷ 2.
On a circular track, bodies in opposite directions meet after track length ÷ sum of speeds.
Always check units before calculating.

Time and Distance practice questions

Time and Distance: frequently asked questions

Is Time and Distance difficult for CMA Foundation?

No. It uses one basic relation with a few variations. Once you learn relative speed and the boat formulas, most questions become routine. Regular timed practice makes them quick.

Which topic in Time and Distance should I start with?

Start with Speed, Distance and Time Basics, including unit conversion and average speed. All the other topics depend on it.

Do I need to memorise many formulas?

Only a small set: distance = speed × time, the 5/18 conversion, average speed, relative speed rules, and upstream and downstream speeds. The rest is applying them carefully.

How long should one Time and Distance MCQ take?

Aim for 30 to 60 seconds. If a question is taking longer, test the options or mark it and return. There is no negative marking, so never leave any question blank.