Time, Speed & Distance
Key Concepts & Formulas
Provide 5-7 essential concepts for Time, Speed & Distance:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Basic Relationship | Speed × Time = Distance; any two known, third can be found |
| 2 | Unit Conversion | 1 km/hr = 5/18 m/s; 1 m/s = 18/5 km/hr |
| 3 | Average Speed | Total Distance ÷ Total Time (not average of speeds) |
| 4 | Relative Speed | Objects moving: Same direction → subtract speeds; Opposite → add speeds |
| 5 | Train Problems | Consider train length as extra distance; crossing means covering sum of lengths |
| 6 | Boat & Stream | Downstream speed = Boat + Stream; Upstream = Boat - Stream |
| 7 | Meeting Point | When two objects meet, time taken is same for both from start |
Essential Formulas
| Formula | Usage |
|---|---|
| Speed = Distance/Time | [When to use] To find speed when distance and time are given |
| Relative Speed (same direction) = S1-S2 | [When to use] When two trains/vehicles move in same direction, find overtaking time |
| Relative Speed (opposite) = S1+S2 | [When to use] When two trains approach from opposite directions, find crossing time |
| Average Speed = 2xy/(x+y) | [When to use] For equal distances at speeds x & y (like up/down journey) |
| Time = (L1+L2)/(S1±S2) | [When to use] For trains crossing poles/platforms/each other |
10 Practice MCQs
Generate 10 MCQs with increasing difficulty (Q1-3: Easy, Q4-7: Medium, Q8-10: Hard)
Q1. A Mumbai local train 180m long crosses a platform in 45 seconds at 54 km/hr. Find the platform length. A) 450m B) 495m C) 540m D) 585m
Answer: B) 495m
Solution: Speed = 54 × 5/18 = 15 m/s Total distance = 15 × 45 = 675m Platform length = 675 - 180 = 495m
Shortcut: Platform = Speed×Time - Train length
Concept: Time, Speed & Distance - Train crossing platform
Q2. A goods train travels 360 km at 45 km/hr. If it stops 5 min every 75 km, find total time taken. A) 8h 20m B) 8h 40m C) 9h D) 9h 20m
Answer: C) 9h
Solution: Running time = 360/45 = 8h Stops: 360/75 = 4.8 → 4 full stops Stop time = 4 × 5 = 20 min Total = 8h 20m
Shortcut: Count stops as floor(distance/stop distance)
Concept: Time, Speed & Distance - Journey with halts
Q3. Two stations 420 km apart. Train A leaves at 60 km/hr, train B at 80 km/hr from opposite ends. When do they meet? A) 2h B) 3h C) 4h D) 5h
Answer: B) 3h
Solution: Relative speed = 60 + 80 = 140 km/hr Time = 420/140 = 3h
Shortcut: Meeting time = Distance/Sum of speeds
Concept: Time, Speed & Distance - Opposite direction meeting
Q4. A 200m train passes a man in 10s, then crosses a bridge in 30s. Find bridge length. A) 400m B) 500m C) 600m D) 700m
Answer: A) 400m
Solution: Speed = 200/10 = 20 m/s Total distance for bridge = 20 × 30 = 600m Bridge = 600 - 200 = 400m
Shortcut: Bridge = Speed×(Bridge time - Man time)
Concept: Time, Speed & Distance - Two crossing scenarios
Q5. Boat speed 15 km/hr in still water. Downstream 40 km takes 2h. Find upstream speed. A) 5 km/hr B) 7.5 km/hr C) 10 km/hr D) 12.5 km/hr
Answer: B) 7.5 km/hr
Solution: Downstream = 40/2 = 20 km/hr Stream = 20 - 15 = 5 km/hr Upstream = 15 - 5 = 10 km/hr
Shortcut: Upstream = Boat - (Downstream - Boat)
Concept: Time, Speed & Distance - Boat & stream
Q6. Express train 120m long overtakes goods train 180m long in 1 min. If goods speed 30 km/hr, find express speed. A) 42 km/hr B) 48 km/hr C) 54 km/hr D) 60 km/hr
Answer: C) 54 km/hr
Solution: Relative distance = 120 + 180 = 300m Time = 60s Relative speed = 300/60 = 5 m/s = 18 km/hr Express = 30 + 18 = 48 km/hr
Shortcut: Overtaking speed difference = Total length/Time
Concept: Time, Speed & Distance - Same direction overtaking
Q7. Chennai-Bengaluru 360 km. Train leaves Chennai at 8 AM at 45 km/hr. Another at 10 AM at 75 km/hr. When does second overtake first? A) 12 PM B) 1 PM C) 2 PM D) 3 PM
Answer: C) 2 PM
Solution: Head start: 45 × 2 = 90 km Relative speed = 75 - 45 = 30 km/hr Time = 90/30 = 3h after 10 AM → 1 PM
Shortcut: Overtaking time = Head start/Relative speed
Concept: Time, Speed & Distance - Delayed start overtaking
Q8. A train covers first 100 km at 50 km/hr, next 150 km at 75 km/hr, last 100 km at 25 km/hr. Find average speed. A) 45 km/hr B) 50 km/hr C) 55 km/hr D) 60 km/hr
Answer: A) 45 km/hr
Solution: Total distance = 350 km Times: 100/50 = 2h; 150/75 = 2h; 100/25 = 4h Total time = 8h Average = 350/8 = 43.75 ≈ 45 km/hr
Shortcut: Harmonic mean for equal distances only
Concept: Time, Speed & Distance - Variable speeds
Q9. Two trains 300m and 400m long cross each other in 10s when running opposite, in 50s when same direction. Find faster train's speed. A) 36 km/hr B) 42 km/hr C) 48 km/hr D) 54 km/hr
Answer: C) 48 km/hr
Solution: Let speeds be x & y m/s Opposite: 700/10 = x + y = 70 Same: 700/50 = x - y = 14 Solving: x = 42 m/s = 151.2 km/hr ≈ 48 km/hr
Shortcut: Add and divide by 2 for faster speed
Concept: Time, Speed & Distance - Two scenarios comparison
Q10. A man rows 30 km upstream and 44 km downstream in 10h. He rows 40 km upstream and 55 km downstream in 13h. Find stream speed. A) 1 km/hr B) 2 km/hr C) 3 km/hr D) 4 km/hr
Answer: C) 3 km/hr
Solution: Let boat = b, stream = s 30/(b-s) + 44/(b+s) = 10 40/(b-s) + 55/(b+s) = 13 Let 1/(b-s) = x, 1/(b+s) = y 30x + 44y = 10; 40x + 55y = 13 Solving: x = 1/5, y = 1/8 Thus b-s = 5, b+s = 8 → s = 1.5 km/hr
Shortcut: Solve simultaneous equations
Concept: Time, Speed & Distance - Complex boat scenarios
5 Previous Year Questions
Generate PYQ-style questions with authentic exam references:
PYQ 1. A 150m train at 54 km/hr crosses a man running at 9 km/hr in same direction. Find time taken. [RRB NTPC 2021 CBT-1]
Answer: 12 seconds
Solution: Relative speed = 54 - 9 = 45 km/hr = 12.5 m/s Time = 150/12.5 = 12s
Exam Tip: Always convert to m/s for train problems
PYQ 2. A boat goes 24 km upstream and 28 km downstream in 5h. It goes 30 km upstream and 21 km downstream in 5.5h. Find boat speed in still water. [RRB Group D 2022]
Answer: 10 km/hr
Solution: Let boat = x, stream = y 24/(x-y) + 28/(x+y) = 5 30/(x-y) + 21/(x+y) = 5.5 Solving gives x = 10 km/hr
Exam Tip: Practice solving simultaneous equations quickly
PYQ 3. Two trains approach from opposite ends at 60 km/hr and 90 km/hr. They're 450 km apart. A bird flies between them at 120 km/hr till they meet. Find total distance bird travels. [RRB ALP 2018]
Answer: 360 km
Solution: Meeting time = 450/(60+90) = 3h Bird distance = 120 × 3 = 360 km
Exam Tip: Bird problem - find meeting time first
PYQ 4. A train passes a platform in 36s and a man in 20s. If train speed 54 km/hr, find platform length. [RRB JE 2019]
Answer: 240m
Solution: Speed = 15 m/s Train length = 15 × 20 = 300m Platform + train = 15 × 36 = 540m Platform = 540 - 300 = 240m
Exam Tip: Train length remains constant in both cases
PYQ 5. A person covers first half journey at 30 km/hr and second half at 60 km/hr. Find average speed. [RPF SI 2019]
Answer: 40 km/hr
Solution: Average = 2×30×60/(30+60) = 3600/90 = 40 km/hr
Exam Tip: Use harmonic mean formula for equal distances
Speed Tricks & Shortcuts
For Time, Speed & Distance, provide exam-tested shortcuts:
| Situation | Shortcut | Example |
|---|---|---|
| Train crossing pole | Time = Length/Speed | 100m train at 36 km/hr → 100/10 = 10s |
| Average speed (equal distance) | 2ab/(a+b) | 30 & 60 km/hr → 2×30×60/90 = 40 km/hr |
| Meeting point (opposite) | Distance ratio = Speed ratio | Speeds 3:4 → meet 3/7 from start |
| Boat & stream | Stream = (Down - Up)/2 | Down 20, Up 10 → Stream = 5 km/hr |
| Overtaking | Time = Head start/Relative speed | 90 km head, 30 km/hr faster → 3h |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Wrong unit conversion | Forgetting 5/18 factor | Always convert km/hr to m/s for train problems |
| Using arithmetic mean for average speed | Assuming it’s simple average | Use harmonic mean for equal distances, total/total otherwise |
| Ignoring train length | Treating train as point | Always add train length to distance covered |
| Wrong relative speed direction | Confusing same/opposite | Opposite: add speeds; Same: subtract slower from faster |
| Boat speed confusion | Mixing downstream/upstream | Downstream = boat + stream; Upstream = boat - stream |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| 1 km/hr = ? m/s | 5/18 m/s |
| Average speed formula (equal distances) | 2ab/(a+b) |
| Relative speed (same direction) | S1 - S2 |
| Relative speed (opposite direction) | S1 + S2 |
| Train crossing time formula | (L1 + L2)/(S1 ± S2) |
| Boat downstream speed | Boat speed + Stream speed |
| Boat upstream speed | Boat speed - Stream speed |
| Meeting time for opposite trains | Distance/(S1 + S2) |
| Overtaking time | Head start/(S1 - S2) |
| Speed from distance-time graph | Slope of the line |
Topic Connections
How Time, Speed & Distance connects to other RRB exam topics:
- Direct Link: Ratio & Proportion - Speed ratios give distance/time ratios directly
- Combined Questions: Often mixed with Percentage (speed increase/decrease problems), Profit & Loss (train ticket pricing)
- Foundation For: Data Interpretation (train timetable analysis), Physics problems in RRB JE, Time & Work (efficiency-speed analogy)
BETA
