Question

a person rowing at the rate of 5km/hr in still water takes thrice as much as time going in 40km upstream as going 40km downstream.find
the speed of the stream

Answer 1

Speed of the boat in water =.5 km/hr

Let the speed of the stream be x km/hr

So, the speed of the boat upstream will be (5-x) km / hr

So, the speed of the boat downstream is (5+x) k/hr

Time given to cover 40 km upstream = 3(time taken to cover dowmstream)

⇒40/ (5-x) km/hr = 3(5+x)

⇒1/(5-x)=3(5+x)

⇒5+x=15-3x

⇒x+3x=15-5

⇒4x=10

⇒X=10/4

⇒X=5/2

∴x=2.5 km/hr

Answer 2

Let speed of stream be 's'

Let speed of boat in still water be 'b'

Speed of boat in still water = b = 5 km/h

Let time taken by the boat in going 40km downstream be t1 and time taken by the boat in going 40km upstream be t2.

Time = distance/speed

t1 = 40/(b+s)

t2 = 40/(b-s)

He takes thrice as much as time going in 40km upstream as going 40km downstream.

→t2 = 3t1

→40/(5-s) = 3(40/(5+s))

→1/(5-s) = 3[1/(5+s)]

→5+s = 3(5-s)

→5+s = 15-3s

→ s+3s = 15-5

→ 4s = 10

→ s = 10/4

→ s = 5/2

Therefore, speed of the stream is 5/2 kmph