Fundamentals of Business Mathematics and Statistics · Time and Distance

Relative Speed and Moving Bodies for CMA Foundation

Updated 10 October 2026 · Fact-checked

Relative speed is the speed of one moving body as seen from another. For opposite directions, add the speeds. For the same direction, subtract the smaller from the larger. Then use time = distance ÷ relative speed to find when two bodies meet or when one overtakes the other.

Understand Relative Speed and Moving Bodies

When two bodies move, the gap between them changes. How fast the gap changes is the relative speed. It is the only speed that matters when you ask, "When will they meet?" or "When will A catch B?"

Take two bodies moving towards each other, say a bus from Pune and a car from Mumbai on the same road. Each one closes part of the gap every hour. The gap shrinks by the sum of their speeds. So for opposite directions (towards each other, or away from each other), the relative speed is the sum of the speeds.

Now take two bodies moving the same way, say a scooter ahead and a car behind. The car gains on the scooter only by the extra speed it has. The gap shrinks by the difference. So for the same direction, the relative speed is the difference of the speeds.

Once you have the relative speed, the problem becomes a simple one: the gap to be covered divided by the relative speed gives the time. The gap is the starting distance between the bodies. For trains, the gap to be covered is the sum of the lengths when they cross each other.

Keep units consistent. Convert km/h to m/s by multiplying by 5/18. Convert m/s to km/h by multiplying by 18/5.

Key formulas to remember

Relative speed, opposite directions: Relative speed = S₁ + S₂; Use when bodies move towards each other or away from each other.
Relative speed, same direction: Relative speed = S₁ − S₂ (S₁ > S₂); Use when the faster body chases or overtakes the slower one.
Time to meet or overtake: Time = Gap to be covered ÷ Relative speed; The gap is the initial distance between them, or the sum of lengths for trains crossing.
km/h to m/s: x km/h = x × 5/18 m/s; Use when distance is in metres and time in seconds.
m/s to km/h: y m/s = y × 18/5 km/h; Use when the answer must be in km/h.
Distance covered by each body at meeting: Distance₁ : Distance₂ = S₁ : S₂; Both bodies travel for the same time before meeting, so distances are in the ratio of speeds.

How to solve Relative Speed and Moving Bodies questions

Follow these steps for any question on two moving bodies.

1Draw a quick sketch. Mark the starting positions and the directions of both bodies.
2Decide: are they moving towards or away from each other (opposite), or in the same direction?
3Make units consistent. Convert km/h to m/s or the other way, as the question needs.
4Find the relative speed: add for opposite directions, subtract for the same direction.
5Find the gap to be covered: the starting distance, or the sum of the lengths for trains crossing.
6Divide gap by relative speed to get the time.
7If the question asks where they meet, multiply one body's speed by that time to get its distance.
8Check that the answer is sensible: the time should be positive and the units should match the options.

Quickest way: Gap ÷ relative speed, with the 5/18 shortcut

When to use it: Use for almost every meeting, overtaking and train-crossing MCQ. It takes under a minute.

Write the relative speed straight away: sum if opposite, difference if same direction.
Pick the unit that avoids fractions. If the speeds are in km/h and the gap in km, stay in km/h.
Convert with 5/18 only when the gap is in metres and the time is in seconds.
Divide the gap by the relative speed.
If two bodies start together and meet, split the distance in the ratio of their speeds. This gives each one's share without more calculation.
Scan the options. Often only one fits the units and the rough size.

Common mistakes in Relative Speed and Moving Bodies

Adding speeds when the bodies move in the same direction.
Students memorise "add" and apply it blindly.
Fix: Check the sketch first. Same direction means subtract. Opposite means add.
Forgetting to convert km/h to m/s when lengths are in metres.
The speed looks ready to use, so students skip the unit check.
Fix: Before dividing, write the units of gap and speed side by side. If they differ, convert using 5/18.
Using only one train's length when two trains cross.
Students think of the trains as points, or focus on one train.
Fix: For two trains crossing each other, the gap is the sum of both lengths.
Subtracting the larger speed from the smaller, giving a negative relative speed.
The order of the numbers in the question is taken as the order of subtraction.
Fix: Always subtract the smaller speed from the larger. Relative speed is positive.
Using 18/5 where 5/18 is needed, or the reverse.
Both factors look alike and are easily swapped.
Fix: Remember that m/s is a smaller number than km/h. Going to m/s, the number must shrink, so multiply by 5/18.
Using the total time when the bodies started at different times.
Students ignore the head start of the first body.
Fix: First find the gap the first body builds in its head start. Then use that gap with the relative speed.

Worked examples

Example 1

Two towns A and B are 300 km apart. A car leaves A at 60 km/h and a truck leaves B at 40 km/h at the same time, driving towards each other. After how many hours do they meet?

Show the solution

They move in opposite directions towards each other, so add the speeds.
Relative speed = 60 + 40 = 100 km/h.
Gap to be covered = 300 km.
Time = 300 ÷ 100 = 3 hours.

Answer: 3 hours

Example 2

A train 150 m long, running at 72 km/h, overtakes a goods train 250 m long, running in the same direction at 36 km/h. How many seconds does it take to completely pass the goods train?

Show the solution

Both move in the same direction, so subtract the speeds.
Relative speed = 72 − 36 = 36 km/h.
Convert to m/s: 36 × 5/18 = 10 m/s.
Gap to be covered = 150 + 250 = 400 m.
Time = 400 ÷ 10 = 40 seconds.

Answer: 40 seconds

Exam tips

Read the direction words carefully. "Towards each other", "opposite" and "crossing" mean add. "Overtakes", "chases" and "same direction" mean subtract.
Check the unit of the answer asked: seconds, minutes or hours. The options are often built to catch a missed conversion.
In train problems, ask whether the other object is a pole, a platform or another train. This decides the gap.
Because there is no negative marking, always mark an option. If stuck, eliminate options that are clearly too large or too small for the speeds given.

Practice questions from Time and Distance

Relative Speed and Moving Bodies: frequently asked questions

What is the formula for relative speed in the same and opposite directions?

For opposite directions, relative speed is the sum of the two speeds. For the same direction, it is the difference between the larger and the smaller speed. Time to meet or overtake is the gap divided by this relative speed.

How do I solve two trains meeting problems?

Find the relative speed by adding the speeds if they approach each other. Then divide the distance between them by that speed. If the trains are crossing, use the sum of their lengths as the distance.

When do I convert km/h to m/s?

Convert when the distance is in metres and the time is in seconds. Multiply km/h by 5/18 to get m/s. If everything is already in km and hours, no conversion is needed.

How do I solve chase problems where one body starts earlier?

First find the distance the first body covers in its head start. That is the gap. Then divide the gap by the difference of the speeds to find how long the chaser takes to catch up.