Question: Speed of a boat in standing water is 18 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is-

Solution:

Given,

Speed of a boat in standing water = 18 kmph

The speed of the stream = 3 kmph

∴ Speed upstream = (18 - 3) kmph

= 15 kmph.

∴ Speed downstream = (18 + 3) kmph

= 21 kmph.

So, Total time taken = (105/15 ) + (105/21) hours

= (7 + 5) hours

= 12 hour

Question: A man walk at a speed of 9 km/h. After every kilometer, he takes a rest of 4 minutes. How much time will he take to cover a distance of 6 km?

Solution:

Given,

Distance = 6 km

Speed = 9 km/h

∴ The man needs time = (Distance ÷ Speed)

= (6 ÷ 9) hours

= 2/3 hours

= (2/3 × 60) minutes

= 40 minutes

He will also rest 4 times after 1000, 2000, 3000, 4000 and 5000 meters

Total resting time = 4 × 5

= 20 minutes.

Total time = (40+ 20) minutes

= 60 minutes

= 1 hour

Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

Solution:

Relative speed of the thief and policeman  =  (11 - 10) km/hr = 1 km/hr 

Distance covered in 6 minutes  = (1/60) × 6 km   = 1/10 km = 100 m

Therefore, Distance between the thief and policeman = (200 - 100) m = 100 m.