Races & Circular Tracks
Races और circular track के sawaal
Races & Circular Tracks
- Speed, Time & Distance
- Races & Circular Tracks
Turn 'beats by' statements into speed ratios and handle basic circular-track meetings.
🎯 Learning Objective
Turn 'beats by' statements into speed ratios and handle basic circular-track meetings.
💡 Concept
- 'A beats B by 20 m in a 100 m race' → when A runs 100, B has run 80 → speeds 100 : 80 = 5 : 4
- 'Beats by d metres OR t seconds' → the loser covers those d metres in t seconds
- Circular track, same direction: first meeting after L/(a − b) seconds
- Circular track, opposite directions: first meeting after L/(a + b) seconds
- Speed ratio = ratio of distances covered in the same time
🧮 Key Formulas
Beats by d: speeds = L : (L − d)
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Circular same: L/(a − b)
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Circular opposite: L/(a + b)
✏️ Easy Example
Q. In a 100 m race, A beats B by 20 m. Find the ratio of their speeds.
- Same time: A runs 100, B runs 80
- Ratio = 100 : 80
Answer: 5 : 4
🇮🇳 Real-Life Example
Two friends jog on the circular walking track of a society park in opposite directions and keep crossing near the same bench — that regular interval is L/(a + b) running quietly every morning.
📝 Exam-Level Example
Q. In a 100 m race, A beats B by 10 m or 2 seconds. Find A's time over the course.
- B runs 10 m in 2 s → B = 5 m/s
- B's full time = 100/5 = 20 s
- A finishes 2 s earlier: 20 − 2
Answer: 18 seconds
📝 Exam-Level Example
Q. Two runners move on a 400 m circular track at 6 m/s and 4 m/s. When do they first meet if running (i) in the same direction (ii) in opposite directions?
- Same: 400/(6 − 4) = 200 s
- Opposite: 400/(6 + 4) = 40 s
Answer: 200 s and 40 s
🪄 Memory Trick
'Beats by d metres or t seconds' — those d metres belong to the LOSER, taking t seconds. Loser's speed = d/t, instantly.
⚠️ Common Mistakes
- ❌ Assigning the beat distance to the winner (it belongs to the loser)
- ❌ Using L/(a − b) for opposite directions
🏆 Exam Tips
- ✅ Speed ratio = distances covered in the same time — write both runners' distances first
- ✅ Meeting again AT the starting point = LCM of lap times, different from the first meeting anywhere
📌 Summary
- Beats by d → speeds L : (L − d)
- d metres or t seconds → loser's speed = d/t
- Circular: same L/(a−b), opposite L/(a+b)
- Start-point reunion = LCM of lap times