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

Time, Speed, Distance, Boats and Trains short notes for CAT: 31 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

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.

Relative Speed: Speed of Closing the Gap

Relative speed = gap-closing speed

Opposite directions

S_{rel} = S_{1} + S_{2}

Same direction

S_{rel} = ∣ S_{1} - S_{2} ∣

Towards Each Other vs Same Direction

Same gap, two relative speeds

Motion type	Relative speed	Distance equation
Towards each other	$S_{1} + S_{2}$	$D = (S_{1} + S_{2}) t$
Same direction chase	$S_{1} - S_{2}$	$D = (S_{1} - S_{2}) t$

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 short notes in this unit

chapter

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

Time, Speed, Distance, Boats and Trains short notes for CAT: 31 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questi

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?

Free preview ends here

Login to view the complete short notes

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free