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Time, speed, distance

Lesson 105 of 113

1. Ye topic hai kya?

Time, speed, distance = sadak/train. Pipes P10 yahi: 60 km, 3 h, speed? S = D/T = 20 km/h. Boat current nahi. Tank leak nahi.

Paper yahan kya maangta

S=D/T, ×5/18, equal-distance harmonic (alag numbers), late/early, stoppage min/h, train pole/platform, opposite/same, do log milna, peeche se catch.

Yahan kya nahi

Still water ± current — Boats (agle). 16 h + 24 h − 48 h leak — Pipes. A 10 B 15 log — Time and work. 3 km east phir north — Direction. 40 km/h & 60, avg 48 — Average.

S = D/T · D = ST · T = D/S
km/h → m/s: × 5/18. m/s → km/h: × 18/5.

2. 60 km, 3 h — 20, 72 km/h — 20 m/s

60/3=20 km/h. 72 km/h = 72×5/18=20 m/s. 10 m/s = 10×18/5=36 km/h. Train lengths metres + seconds — pehle m/s.

0 h 1 h · 20 km 2 h · 40 3 h · 60 20 km/h seedha

Har ghante +20 km. Pipes tank / leak yahan nahi.

120 km, 40 km/h → 3 h; 60 km/h → 2 h; farq 1 h.

Example

60 km, 3 h. Speed? (Pipes P10.)

Solution

  1. 60/3

    20 km/h. 20 L/min Pipes nahi.

Answer20 km/h
Example

72 km/h = ? m/s

Solution

  1. ×5/18

    20 m/s. ×18/5 mat.

Answer20 m/s

3. Average speed, late, stoppage

Equal time do speeds: arithmetic mean. 20 aur 30, 1–1 h → 25 km/h.

Equal distance: harmonic 2xy/(x+y). 20 aur 30, 20–20 km → 2×20×30/50 = 24 km/h, 25 nahi. (Average-page 40&60=48 yahan copy nahi.)

5 km/h se 10 min late, 6 km/h se 10 min early. Farq 20 min = 1/3 h. d/5 − d/6 = 1/3 → d/30 = 1/3 → d=10 km.

Bina ruk 54 km/h, ruk ke 45. Stoppage per hour = (54−45)/54 × 60 = 10 min.

Example

20 km @20 km/h, 20 km @30. Avg?

Solution

  1. 2xy/(x+y)

    24. 25 equal-time. 48 Average 40-60.

Answer24 km/h
Example

5 km/h 10 min late, 6 km/h 10 min early. d?

Solution

  1. d/30=1/3

    10 km.

Answer10 km

4. Train, milna, catch

Pole/aadmi: sirf train ki length. Platform: train + platform. Opposite: lengths jodo, speed jodo. Same direction: speed ghao.

180 m train, 54 km/h = 15 m/s. Pole: 180/15=12 s. Platform 120 m: 300/15=20 s.

180 m pole 54 km/h = 15 m/s · 12 s

Engine se guard tak pole. Boat length nahi. 3 km east nahi.

Do trains 180 m + 120 m, opposite 54 aur 36 km/h: 90 km/h = 25 m/s, 300/25=12 s. Same direction: 18 km/h = 5 m/s, 300/5=60 s.

200 km door, 40 aur 60 opposite: relative 100, milna 2 h. A 80 km chala.

A 40 km/h, 1 h baad B 60 same road: gap 40 km, relative 20, catch 2 h (B start ke 2 h baad).

Train pe km/h ko m/s kiye bagair metre/second mat. Equal distance pe (x+y)/2 mat. Upstream Boats. Leak Pipes. 3 km east–north Direction / Coordinate.
Example

180 m, 54 km/h, pole. Time?

Solution

  1. 15 m/s

    12 s. Platform 20 s alag.

Answer12 s
Example

200 km, 40 aur 60 opposite. Kab milen?

Solution

  1. 200/100

    2 h.

Answer2 h

5. Sawal — basic se pro

Q1 · Basic

60 km, 3 h. Speed?

  1. 20 km/h
  2. 18 km/h
  3. 63 km/h
  4. 20 m/s

Solution

  1. 20

    D 72 km/h wala.

Answer20 km/h
Q2 · Basic

72 km/h → m/s?

  1. 20
  2. 12.96
  3. 259.2
  4. 18

Solution

  1. ×5/18

    20. C ×18/5.

Answer20
Q3 · Basic

10 m/s → km/h?

  1. 36
  2. 50/18
  3. 18
  4. 10

Solution

  1. ×18/5

    36.

Answer36
Q4 · Medium

Equal d, 20 aur 30 km/h. Avg?

  1. 24
  2. 25
  3. 48
  4. 50

Solution

  1. 24

    B equal-time. C Average 40-60.

Answer24
Q5 · Medium

120 km, 40 vs 60 km/h. Time farq?

  1. 1 h
  2. 2 h
  3. 3 h
  4. 5 h

Solution

  1. 3−2

    1 h.

Answer1 h
Q6 · Medium

180 m, 54 km/h, pole?

  1. 12 s
  2. 20 s
  3. 3.33 s
  4. 10 s

Solution

  1. 180/15

    12. B platform 120 m.

Answer12 s
Q7 · Medium

Usi train + 120 m platform?

  1. 20 s
  2. 12 s
  3. 8 s
  4. 30 s

Solution

  1. 300/15

    20.

Answer20 s
Q8 · Pro

5 km/h 10 min late, 6 early 10 min. d?

  1. 10 km
  2. 11 km
  3. 30 km
  4. 1 km

Solution

  1. d/30=1/3

    10.

Answer10 km
Q9 · Pro

54 km/h without stop, 45 with. Stop min per h?

  1. 10
  2. 9
  3. 15
  4. 6

Solution

  1. 9/54 × 60

    10.

Answer10
Q10 · Pro

16 h, 24 h fill, 48 h leak → 12 h. Is chapter?

  1. Nahi — Pipes
  2. Haan, 12 km/h
  3. Train 12 s
  4. Avg 12

Solution

  1. Tank

    A. Wahan net 12 h.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

Equal time, 20 aur 30. Avg?

  1. 25
  2. 24
  3. 50
  4. 15

Solution

  1. (20+30)/2

    25. B equal-d.

Answer25
P2

200 km, 40+60 opposite. Time?

  1. 2 h
  2. 5 h
  3. 3.33 h
  4. 100 h

Solution

  1. 200/100

    2.

Answer2 h
P3

A 80 km kahan (usi meet)?

  1. 80 km from A
  2. 120 km from A
  3. 100
  4. 40

Solution

  1. 40×2

    80. B B ka 120.

Answer80 km from A
P4

180+120 m, opposite 54 & 36 km/h. Time?

  1. 12 s
  2. 60 s
  3. 8.57 s
  4. 20 s

Solution

  1. 300/25

    12. B same-dir 60 s.

Answer12 s
P5

Same trains, same direction?

  1. 60 s
  2. 12 s
  3. 30 s
  4. never

Solution

  1. 300/5

    60.

Answer60 s
P6

A 40 km/h, 1 h baad B 60. Catch?

  1. 2 h after B starts
  2. 2 h after A
  3. 4 h
  4. 40 min

Solution

  1. 40/20

    2 h after B. B 3 h total A.

Answer2 h after B starts
P7

90 km/h → m/s?

  1. 25
  2. 18
  3. 50
  4. 324

Solution

  1. 90×5/18

    25. Opposite trains wahi 25.

Answer25
P8

16 h + 24 h − leak 48 h. Is chapter?

  1. Nahi — Pipes
  2. Haan, 12 km
  3. Train 12
  4. Stoppage 12

Solution

  1. Tank

    A.

AnswerA
P9

Still 12 km/h, current 4, down 16 up 8. Is chapter?

  1. Nahi — Boats
  2. Haan, 12 km/h TSD
  3. Train 16
  4. Avg 12

Solution

  1. Paani

    A. Agle pe.

AnswerA
P10

3 km east, 4 km north, net 5 km. Is chapter?

  1. Nahi — Direction
  2. Haan, 5 km/h
  3. Train 5
  4. Coordinate TSD

Solution

  1. Map

    A. Reasoning Direction. Coordinate √(x²+y²) Maths pe.

AnswerA

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Agle topic: Boats and streams.