Time, Speed & Distance: The Complete Concept Blog

Hey there! If you’re preparing for banking, SSC, or any competitive exam, Time, Speed & Distance (TSD) is one of those topics that keeps coming back—sometimes directly, sometimes mixed with trains, boats, circular tracks, or races. The good news is that once you understand the core ideas, most questions become just a few steps of logical math. In this blog, I’ll walk you through every important concept from basic to advanced, including circular tracks and races. 

Let’s dive in.

1. The Three Pillars: Speed, Distance, Time

Everything in TSD revolves around one simple formula:

From this, we get:

Example:
A car covers 150 km in 3 hours.
Speed = 150 / 3 = 50 km/h.

Unit conversion:

• 1 km/h = 5/18 m/s
• 1 m/s = 18/5 km/h

So, 90 km/h = 90 × 5/18 = 25 m/s.
And 20 m/s = 20 × 18/5 = 72 km/h.

2. Ratio & Proportionality Rules

These rules save you from long calculations.

When Time is Constant

Speed and Distance are directly proportional.

Example:
Two friends run for the same time. Speeds are 4 km/h and 5 km/h.
Distance ratio = 4 : 5.

When Distance is Constant

Speed and Time are inversely proportional.

Example:
A covers 60 km at 30 km/h, B covers 60 km at 20 km/h.
Speed ratio = 30 : 20 = 3 : 2.
Time ratio = 2 : 3.

When Speed is Constant

Distance and Time are directly proportional.

3. Average Speed

Average speed is not the average of speeds. It is:

Special Case: Equal Distances

If a person travels the same distance at speeds and , then:

Example:
Up hill at 30 km/h, down hill at 20 km/h.
Average = km/h.

Different Distances

Just add distances and times.

Example:
120 km at 40 km/h → 3 hr
180 km at 60 km/h → 3 hr
Total distance = 300 km, total time = 6 hr.
Average = 300 / 6 = 50 km/h.

4. Relative Speed

When two objects move:

• Opposite direction: Relative Speed =
• Same direction: Relative Speed =

Time to meet = Initial distance / Relative speed.

Example 1 (Opposite):
Two trains 300 km apart, speeds 60 km/h and 40 km/h.
Relative speed = 100 km/h.
Time = 300 / 100 = 3 hours.

Example 2 (Same direction):
A thief runs at 50 km/h, police at 70 km/h. Gap = 60 km.
Relative speed = 20 km/h.
Time = 60 / 20 = 3 hours.

5. Early, Late & Scheduled Time

If a person travels at two different speeds and reaches early or late, use:

• If one case is early and the other is late, add the times.
• If both are early or both are late, subtract the times.

Example:
At 60 km/h, A reaches 20 min early.
At 45 km/h, A reaches 10 min late.
Time difference = 20 + 10 = 30 min = 0.5 hr.

So the distance is 90 km.

6. Meeting Point Problems

When two people start from opposite ends and meet, time is the same for both.
So, Distance ratio = Speed ratio.

Example:
A and B start from X and Y towards each other.
Speeds: A = 7 km/h, B = 3 km/h. Total distance = 200 km.
Distance ratio = 7 : 3.
A covers km.
B covers 60 km.

Same Direction & Head Start

Convert head start into distance gap.
Then use relative speed = difference.

7. After-Meeting Formula

If two people meet and then continue to their destinations, and after meeting they take and hours respectively:

Example:
After crossing, A takes 16 hours to reach B’s start, B takes 9 hours to reach A’s start.

So, speed ratio A : B = 3 : 4.

8. Segmented & Variable Speed Journeys

When a journey is split into parts with different speeds:

Example:
A bus covers 120 km at 60 km/h and next 120 km at 40 km/h.
Time = 2 + 3 = 5 hours.
Average speed = 240 / 5 = 48 km/h.

If speed changes after an accident, the delay is caused only by the remaining distance.
Set up equations using the reduced speed.

9. Circular Track Concepts

On a circular track of circumference :

Same Direction

• First meeting time =
• Meeting at starting point: time = LCM of their individual lap times.

Example:
Track = 600 m. Speeds = 10 m/s and 15 m/s (same direction).
Relative speed = 5 m/s.
First meet = 600 / 5 = 120 seconds.
Lap times: 60 s and 40 s.
LCM = 120 s → they meet at starting point after 120 seconds.

Opposite Direction

• First meeting time =

Example:
Same track, speeds 10 and 15 opposite.
Relative speed = 25 m/s.
Time = 600 / 25 = 24 seconds.

Multiple Meetings

• Opposite direction: nth meeting total distance =
• Same direction (from same point): nth meeting total distance =

10. Race Concepts

Beating by Distance

If A beats B by meters in a race of meters, then when A finishes , B covers .
Speed ratio:

Example:
In 800 m race, A beats B by 80 m.
A : B = 800 : 720 = 10 : 9.

Beating by Time

If A beats B by seconds, then B takes seconds more to finish after A finishes.
Use .

Example:
In 1000 m race, A beats B by 100 m or 25 seconds.
B’s speed = 100 / 25 = 4 m/s.
B’s time = 1000 / 4 = 250 s.
A’s time = 250 – 25 = 225 s.

Start / Lead

If A gives B a start of meters in race of :

Combined Race Ratios

If A beats B and B beats C, multiply ratios to find A : C.

Example:
In 600 m, A beats B by 60 m → A:B = 600:540 = 10:9.
In 500 m, B beats C by 50 m → B:C = 500:450 = 10:9.
Then A:C = (10/9) × (10/9) = 100:81.
In 400 m race, A beats C by m.

11. Advanced & Mains Patterns

Partial Journey with Two Modes

Let be variables. Form equations from total time.

Example:
Total 500 km.
Case 1: 200 km by bus + 300 km by car = 8 hr.
Case 2: 300 km by bus + 200 km by car = 9 hr.
Solve to get bus and car speeds.

Complex Multi-Day Problems

Break the information into equations.
Use consistent variables for speeds and distances.

After-Meeting with Multiple People

Use the same after-meeting formula, but apply it pairwise.

Circular Track Races

If a race is to end on the nth meeting, total distance = relative speed × time.

12. Quick Formula Cheat Sheet

13. Final Thoughts

Time, Speed & Distance is not about memorizing dozens of formulas. It’s about understanding a few core relationships:

• Distance = Speed × Time
• Ratios change depending on what is constant
• Relative speed is the key to meeting problems
• Circular tracks and races are just applications of these basics

Practice with different numbers, and soon you’ll see the pattern behind every question. Happy learning!