Two train leaves New Delhi at the same time. One travels towards North at 60 km/h and the other travels towards South at 40 km/h . After how many hours will the trains be 150 km apart?

Distance = 160 km
Relative Speed = 8 + 2 = 10
Time = Distance/Relative speed = 160/10 = 16 h

Let speed of walking be V km/h.
Total time taken = (7.5/3) + 2 = 4.5 h
Total distance covered = (7.5 + 2V) km
? (7.5 + 2V)/4.5 = 4
? 7.5 + 2V = 18
? 2V = 10.5
? V = 5.25
? Speed of walking = 5.25 km/h

Number of gaps between 25 telephone posts = 24
Distance travelled in 1 min = 40 x 24 = 960 m
Speed = (960 x 60)/1000 = 57.6 km/h

Let total distance covered in the whole journey = L km
? 2L/25 + 21L/50 + 2 = L
? L = 4
? Total distance covered = 4 km

Relative speed of express train to local train = 65 - 29 = 36 km/h
= 36 x (5/18) m/s = 10 m/s
? Length of faster train = 10 x 16 = 160 m

Since, the boys now walks at 5/7 of usual speed, so he will take 7/5 of his usual time.
? Extra time = (7/5 - 1) x Usual time = 6 min (known)
? 2/5 x Usual time = 6
? Usual time = 15 min

Average speed = [(30/60) x 40 + (45/60) x 60 + (2 x 70)] / [(30/60) + (45/60) + 2]
= (20 + 45 + 140)/[(30 + 45 + 120)/60]
= (205/195) x 60 km/h
= 63.07 km/h
= 63 km/h

New speed = 8/11 of usual speed
New time = 11/8 of usual time
? 11/8 of usual time = 11/2 h
? Usual time = (11 x 8)/(2 x 11) = 4 h
? Time saved = 5¹/₂- 4
= 1¹/₂

Let the distance be D km
Difference in timings = 8 min = 8/60 h = 2/15 h
? D/3 - D/4 = 2/15
? D/12 = 2/15
? D = 2 x 12/15 = 1.6 km

Relative speed of policeman with thief = (10 - 8) = 2 km/h
Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h

Now, Speed = Distance / Time
? Time = D/S = 100/2000
= 1/20 h or 60/20 min = 3 min