GMAT Quant: Time-Speed-Distance: Relative Speed

50 Words Summary

Relative speed equals the sum of speeds in opposite directions and the difference in the same direction. Example: two cars 210 km apart, speeds 40 and 30 km/h. Opposite directions: time to meet = 210 ÷ (40+30) = 3 hours. Same direction: time = 210 ÷ (40−30) = 21 hours.

Overview

Relative speed is one of those ideas that feels simple but can easily trip you up if not understood deeply. The key lies in recognizing that when two objects move in opposite directions, their speeds add up, and when they move in the same direction, their speeds subtract. This principle, though basic, forms the foundation of many complex-looking GMAT questions. Take trains for example. When they cross each other, the effective distance is the sum of their lengths, and the relative speed determines the time required. Even when one is stationary, or when the situation involves crossing a pole or a platform, the same logic holds true. Understanding this helps you see through what might otherwise look like long, confusing word problems. To strengthen this topic further, master it during your GMAT preparation course and practice it in GMAT full-length mock tests for exam-like application.

Understanding Relative Speed

Relative speed is defined as the sum of speeds when two bodies move in opposite directions and the difference of speeds when they move in the same direction. This principle allows us to handle a wide variety of motion problems with clarity and accuracy.

Worked Example with Multiple Cases

Consider this problem: A train 100 meters long moves east to west at 20 meters per second.

Case 1: Opposite Direction with Another Train

A second train, 200 meters long, moves west to east at 10 meters per second.

 The distance between them is 600 meters.

• Total distance to cover = 600 + 200 + 100 = 900 meters.
• Relative speed = 20 + 10 = 30 meters per second.
• Time = 900 ÷ 30 = 30 seconds.

Case 2: Same Direction

If the second train moves east to west at 10 meters per second,

• Total distance remains 900.
• Relative speed = 20 – 10 = 10 meters per second.
• Time = 900 ÷ 10 = 90 seconds.

Case 3: Stationary Train

If the second train is stationary,

• Distance = 900 meters.
• Speed = 20 meters per second.
• Time = 900 ÷ 20 = 45 seconds.

Case 4: Crossing a Pole

If the train must cross a pole located 1,000 meters ahead,

• Distance = 1,000 + 100 = 1,100 meters.
• Speed = 20 meters per second.
• Time = 1,100 ÷ 20 = 55 seconds.

Key Takeaway

These cases illustrate how relative speed transforms seemingly different questions into straightforward calculations. The secret lies in always defining the total distance correctly and then applying either the sum or difference of speeds. To practice such questions under timed conditions, make sure you work through our GMAT-style simulation, which provides structured exposure to speed, distance, and motion problems.

Parting Thought

Relative speed teaches alignment. Progress accelerates when forces move in the same direction and stalls when they pull apart. In GMAT preparation, choose study blocks, revision, and timed practice that add pace together; remove habits that subtract it. In the MBA applications procedure, align essays, recommendations, and achievements so their vectors point to one purpose; contradictions slow you down. In life, pick companions, routines, and commitments that carry you toward your goals, and release frictions that pull you back. Keep asking, am I adding speed or cancelling it. Direction first, then pace. When alignment is right, distance covered per minute rises.