Advanced Analytical Skills — II

Unit 5: Advanced TSD & Races

Master Time-Speed-Distance, unit conversions, average speed via harmonic mean, late/early puzzles, ratio methods, linear races, relative speed, and boats & streams — with 15 worked examples and 41 practice questions.

⏱️ Time to Complete: 6–8 hours | 📝 30 MCQs + 8 Short + 3 Long (Bloom's Mapped) | 📐 Full Formula Sheet

🎯 Exams this covers: CAT · XAT · SNAP · MAT · CMAT · SSC CGL · Bank PO · GATE (Aptitude) · Placement Tests

Section 1

Opening Hook — When Speed Decides Everything

🚄 The Mumbai–Ahmedabad Bullet Train Problem

India's first bullet train will cover 508 km between Mumbai and Ahmedabad. At a top speed of 320 km/h, the journey takes roughly 2 hours. But the current Shatabdi Express covers the same route at an average of 80 km/h, taking over 6 hours. How much time does the bullet train save? What if the Shatabdi increased its speed by 25% — how much earlier would it arrive?

These aren't textbook-only questions. Railway engineers, logistics planners at Flipkart, Delhivery route optimisers, and ISRO trajectory scientists solve Time-Speed-Distance (TSD) problems every day. When Zomato promises "30-min delivery," behind it is a real-time TSD algorithm crunching relative speeds, traffic data, and distances.

This chapter gives you the toolkit to solve any TSD problem — from simple unit conversion to advanced races, boats & streams, and two-variable problems.

🚄 Bullet Train Project🇮🇳 Indian Railways📦 Delhivery🛵 Zomato🚀 ISRO

Usain Bolt's 100m world record (9.58s) translates to 37.58 km/h. In a race, if Bolt gave you a 20m head start, he'd still beat you — unless you can run the remaining 80m in under 7.66 seconds. That's the mathematics of races, and you'll learn to solve such problems in this chapter.

Section 2

Learning Outcomes — Bloom's Taxonomy Mapped

Bloom's Level	Learning Outcome
🔵 Remember	Recall the TSD formula, unit conversion factors (km/h ↔ m/s), and race terminology (head start, dead heat)
🔵 Understand	Explain why harmonic mean (not arithmetic mean) is used for average speed when distances are equal
🟢 Apply	Solve late/early problems using the standard shortcut formula; convert between speed units fluently
🟢 Analyse	Break down two-variable TSD problems (boats & streams, moving platforms) into relative speed components
🟠 Evaluate	Compare alternate approaches (algebraic vs ratio) to determine the most efficient solution path
🟠 Create	Formulate original race and TSD problems and construct complete solutions with all steps