Time, Speed, Distance, Boats and Trains Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Time, Speed, Distance, Boats and Trains notes for CAT: 74 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Time, Speed, Distance, Boats and Trains

↔

Chapter Journey

Time, Speed, Distance, Boats and Trains

Step 1 • 11 CAT PYQs • Importance 0.76

🚶 Linear Motion and Relative Speed

Master distance-speed-time, meetings, chases, speed changes, stoppages, and multi-person motion.

Step 2 • 2 CAT PYQs • Importance 0.30

🚣 Boats, Streams and Water Travel

Apply upstream-downstream logic using still-water speed and stream speed.

Step 3 • 3 CAT PYQs • Importance 0.35

🚆 Trains, Crossings and Track Problems

Handle train lengths, poles, platforms, and opposite-direction crossings.

Step 4 • 3 CAT PYQs • Importance 0.35

🕒 Clocks, Circular Motion and Escalators

Convert movement into relative angular speed or effective speed on moving platforms.

By the end of this chapter: you should be able to convert every motion story into distance covered, time taken, and speed used.

Linear Motion and Relative Speed

Arithmetic → Time, Speed, Distance, Boats and Trains → Topic 1

Linear Motion and Relative Speed

Motion questions become easy when you track who covers which distance in whose time.

D=ST

Basic distance-speed-time

Meeting and chasing

Speed-change equations

CAT relative-speed patterns

The One Formula Behind Everything

Distance = Speed × Time

D = S \times T

Distance

How far someone travels.

Speed

Distance covered per unit time.

Time

How long the motion lasts.

Unit Conversion: CAT’s Silent Trap

Convert before solving

km/h to m/s

1 km/h = \frac{5}{18} m/s

m/s to km/h

1 m/s = \frac{18}{5} km/h

Example:

960

meters per minute

= 57.6

km/h because

960 \times 60 = 57600

meters per hour.

Time, Speed, Distance, Boats and Trains: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Ability MCQ

A car travels at a constant speed of $60$ km/h for $2.5$ hours. What is the total distance covered by the car in kilometers?

A.
120
B.
150
C.
180
D.
200

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct application of the fundamental distance formula, recognisable because speed and time are given, and distance is asked.

Step 1: Identify the given values. Speed $S = 60$ km/h, Time $T = 2.5$ hours.

Step 2: Use the formula $Distance = Speed \times Time$ .

Step 3: Calculate $D = 60 \times 2.5 = 150$ km.

Answer: 150

Question 2 · Quantitative Ability MCQ

The "Final CAT Checklist" helps you map problem statements to methods. If a question asks for the time when two runners starting together on a circular track meet for the first time anywhere on the track while running in the same direction, which method does the checklist prescribe?

A.
LCM of their individual lap times
B.
Track Length divided by Sum of Speeds
C.
Harmonic Mean of their lap times
D.
Track Length divided by Relative Speed (Difference)

Correct Answer:

Step-by-Step Solution

Key idea: This is a pattern recognition question, recognisable because it asks to match a specific circular motion scenario to its correct mathematical method.

Step 1: Analyze the conditions: "circular track", "same direction", and "meet anywhere" (not specifically at the start).

Step 2: Recall the rules for circular motion. Meeting at the starting point requires LCM of lap times. Meeting anywhere on the track requires relative speed.

Step 3: Since they run in the same direction, their relative speed is the difference of their speeds ( $S_{1} - S_{2}$ ).

Step 4: The time to meet for the first time anywhere is the Track Length divided by this Relative Speed.

Answer: Track Length divided by Relative Speed (Difference)

More notes in this unit

chapter

Time, Speed, Distance, Boats and Trains Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Time, Speed, Distance, Boats and Trains notes for CAT: 74 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

A question from this chapter

Question 1

A car travels at a constant speed of 60 km/h for 2.5 hours. What is the total distance covered by the car in kilometers?

Question 2

The "Final CAT Checklist" helps you map problem statements to methods. If a question asks for the time when two runners starting together on a circular track meet for the first time anywhere on the track while running in the same direction, which method does the checklist prescribe?

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