29.  A boat takes 2 hours to go 40 km down the stream and it returns in 4 hours. Find the speed of boat in still water and the speed of the stream.
30. A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48minute longer to cover the same distance against the current. Find the speed of boat on still water and the speed of the current.

29 ) Let the speed of the boat in still water be u km/hr and speed of stream be v km/hr.

Speed down the stream = u + v

Speed against the stream = u – v

Now,

Downstream distance = (Speed down the stream) × (Time taken)

⇒ 40 = (u + v) 2

⇒ u + v = 20

⇒ u = 20 – v

Upstream distance = (Speed against the stream) × (Time taken)

⇒ 40 = (u – v) 4

⇒ u – v = 10

⇒ 20 – v – v = 10

⇒ 20 – 2v = 10

⇒ 2v = 20 – 10

⇒ 2v = 10

⇒ v = 5 km/hr

u = 20 – 5 = 15 km/hr

Thus speed of the boat in still water is 15 km/hr and speed of stream is 5 km/hr.

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