How to Solve Relative Speed Problems
Solve relative speed aptitude problems using the sum/difference rule and the stationary-reframe technique, with a worked example and practice questions.
Expected Interview Answer
Relative speed is the speed at which the gap between two moving bodies changes, calculated as the sum of their speeds when moving toward each other or in opposite directions, and as the difference of their speeds when moving in the same direction.
The core idea is to switch reference frames: instead of tracking two moving objects separately, imagine one object is stationary and the other moves at the relative speed. For opposite directions or objects approaching each other, the gap closes fast, so relative speed = speed1 + speed2. For the same direction, the faster object only gains ground at the rate it exceeds the slower one, so relative speed = speed1 − speed2. Once relative speed is found, ordinary distance/speed/time reasoning applies to the gap between the two objects. This single reframing technique underlies trains crossing, boats and streams, and two-runner problems alike.
- One reframing trick (treat one object as stationary) unifies many problem types
- Sum vs difference is a simple direction-based decision
- Extends cleanly to circular-track and meeting-point problems
AI Mentor Explanation
Two fielders converging from opposite corners of the ground to reach a ball close the distance at the sum of their running speeds — from either fielder's point of view, the other appears to approach at that combined rate. If instead one fielder is backing up another running the same direction, the gap between them changes only at the difference of their speeds. This “how fast does the gap change” question is exactly what relative speed answers, whether for fielders or any two moving bodies.
Worked example
Relative speed
- 40 + 30 = 70 km/h
Gap distance
- 210 km
Time to meet
- 210 / 70 = 3 hours
Step-by-Step Explanation
Step 1
Identify direction
Opposite/toward each other → add speeds; same direction → subtract speeds.
Step 2
Compute relative speed
Ensure both speeds share the same unit before combining.
Step 3
Reframe as one moving body
Treat one object as stationary and the other as moving at the relative speed.
Step 4
Apply distance/speed/time
Use the gap distance and relative speed to find time, or vice versa.
What Interviewer Expects
- Correct sum-vs-difference decision based on direction
- The reframing technique of treating one body as stationary
- Consistent unit conversion before combining speeds
- Applying the same logic across trains, boats, and runner problems
Common Mistakes
- Subtracting speeds when objects move toward each other (should add)
- Adding speeds when objects move in the same direction (should subtract)
- Forgetting to convert both speeds to the same unit
- Confusing relative speed with the average of the two speeds
Best Answer (HR Friendly)
“I figure out the direction first — toward each other or opposite directions means I add the two speeds, same direction means I subtract them — because that combined value is how fast the gap between them is actually closing. Then I treat one object as if it were standing still and apply ordinary speed, distance, and time reasoning to the other using that relative speed. This one technique covers trains, boats, and two people walking toward or away from each other.”
Follow-up Questions
- How does relative speed apply to circular track meeting problems?
- How would you find the time for two runners to meet for the second time on a loop?
- How does relative speed change if one object is accelerating?
- How do boats-and-streams problems use the same relative speed concept?
MCQ Practice
1. Two cyclists 100km apart ride toward each other at 20 km/h and 30 km/h. How long until they meet?
Relative speed = 20+30 = 50 km/h. Time = 100/50 = 2 hours.
2. Two joggers start at the same point and jog in the same direction at 8 km/h and 5 km/h. After 2 hours, how far apart are they?
Relative speed = 8−5 = 3 km/h. Distance after 2 hours = 3×2 = 6 km.
3. When two bodies move in the same direction, relative speed equals?
Same-direction motion means the gap changes at the difference of the two speeds.
Flash Cards
Relative speed, opposite directions? — Sum of the two speeds.
Relative speed, same direction? — Difference of the two speeds.
Key reframing trick? — Treat one moving body as stationary and reason about the other.
What does relative speed measure? — The rate at which the gap between two moving bodies changes.