How to Solve: Time, Speed, and Distance Problems

How to Solve: Time, Speed, and Distance Problems

(Complete Guide for SSC/Bank/Railway Exams)

Introduction

"Mastering Time, Speed, and Distance problems can add 5–10 marks to your SSC/Bank/Railway exam—because these questions appear in every section, from Quant to Reasoning! (On camera: Hold up a past paper with a circled TSD question.) "Imagine missing a train by 5 minutes because you miscalculated speed—or losing marks because you mixed up units. Today, we’ll make sure that never happens."

What You Need To Know First

Before diving in, ensure you’re comfortable with: 1. Basic algebra (solving for one variable). 2. Unit conversions (km/h to m/s, hours to minutes). 3. Ratio and proportion (if two objects move at speeds in a ratio, their times/distances follow a pattern).

(On camera: Quick check-in) "Raise your hand if you can convert 72 km/h to m/s in 5 seconds. [Pause] The answer is 20 m/s—we’ll practice this later!

Key Vocabulary

(On camera: Point to the table) "Memorize these terms—exam questions will use them exactly like this. No surprises!

Formulas To Know

(On camera: Write formulas on a whiteboard, one by one.) "These are your weapons. Write them down now—don’t just read them. The first three are the same formula rearranged. The rest are shortcuts to save time in the exam."

Step-by-Step Method

Follow these exact steps for every Time-Speed-Distance problem:

1. Read the question twice. Underline the unknown (what you need to find).
2. List the given data. Write down all numbers with units (km/h, m/s, hours, minutes).
3. Convert units if needed. Ensure all units match (e.g., convert km/h to m/s if distance is in meters).
4. Choose the right formula. Pick from the list above based on what’s given/asked.
5. Plug in the numbers. Write the equation clearly.
6. Solve for the unknown. Show every step—no mental math!
7. Check units and logic. Does the answer make sense? (e.g., speed can’t be negative.)

(On camera: Demonstrate with a simple example) "Let’s try this together. A car travels 150 km in 3 hours. What is its speed?" - Step 1: Unknown = speed. - Step 2: Given = 150 km (distance), 3 hours (time). - Step 3: Units match (km and hours). - Step 4: Use Speed = Distance / Time. - Step 5: Speed = 150 km / 3 h = 50 km/h. - Step 6: Answer = 50 km/h. - Step 7: Check: 50 km/h is reasonable for a car.

Worked Examples

Example 1 – Basic

Question: A train covers 240 km in 4 hours. Find its speed in m/s. Solution: 1. Unknown: Speed in m/s. 2. Given: Distance = 240 km, Time = 4 hours. 3. Convert km to meters: 240 km = 240,000 m.
Convert hours to seconds: 4 hours = 4 × 3600 = 14,400 s. 4. Formula: Speed = Distance / Time. 5. Speed = 240,000 m / 14,400 s = 16.67 m/s. 6. OR (shortcut): First find speed in km/h → 240 km / 4 h = 60 km/h.
Then convert to m/s: 60 × (5/18) = 16.67 m/s. Answer: 16.67 m/s.

What we did and why: - We converted units first to avoid mistakes later. - Used the shortcut (km/h to m/s) to save time—this is critical in exams.

Example 2 – Medium

Question: Two trains start from stations A and B, 300 km apart, and move towards each other at 60 km/h and 40 km/h. How long until they meet? Solution: 1. Unknown: Time until they meet. 2. Given: Distance = 300 km, Speed₁ = 60 km/h, Speed₂ = 40 km/h. 3. Units match (km and km/h). 4. Formula: Relative speed (opposite direction) = S₁ + S₂ = 60 + 40 = 100 km/h.
Time = Total Distance / Relative Speed. 5. Time = 300 km / 100 km/h = 3 hours. Answer: 3 hours.

What we did and why: - Recognized they’re moving towards each other → speeds add. - Used relative speed to simplify the problem (no need to track both trains separately).

Example 3 – Exam-Style

Question: A thief runs at 10 m/s. A policeman starts chasing him 30 seconds later at 15 m/s. How far will the policeman run before catching the thief? Solution: 1. Unknown: Distance policeman runs. 2. Given: Thief’s speed = 10 m/s, Policeman’s speed = 15 m/s, Head start = 30 s. 3. Convert head start to distance: Thief’s head start = 10 m/s × 30 s = 300 m. 4. Relative speed (same direction) = 15 – 10 = 5 m/s. 5. Time to catch up = Distance / Relative Speed = 300 m / 5 m/s = 60 s. 6. Distance policeman runs = 15 m/s × 60 s = 900 m. Answer: 900 meters.

What we did and why: - Calculated the thief’s head start first (critical step!). - Used relative speed to find the time difference. - Multiplied policeman’s speed by time to get distance.

Common Mistakes

(On camera: Hold up a red pen) "These mistakes cost marks. Circle the units and underline the unknown every time."

Exam Traps

(On camera: Show a past paper question with a trap.) "See this? The question says ‘a train stops for 10 minutes.’ If you ignore that, your answer is wrong. Always check for stops/delays!

1-Minute Recap

(On camera: Speak directly to the student, fast but clear.)

"Listen up—this is your last-minute checklist: 1. Formula first: Speed = Distance / Time. Write it down now. 2. Units matter: Convert km/h to m/s with ×(5/18). No excuses. 3. Relative speed: Same direction? Subtract speeds. Opposite? Add them. 4. Average speed: Total distance over total time—not the average of speeds. 5. Read twice: Underline the unknown and given data. Circle the units. 6. Practice 3 problems tonight: One basic, one relative speed, one with unit conversion.

You’ve got this. Go solve one problem right now—no peeking at the solution!