Question

The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. The speed of this stream (in km/hr) will be:

Answer 1

Answer:

Let the speed of the stream be x km/hr

Then,

Speed downstream = (15 + x) km/hr

Speed upstream = (15 - x) km/hr

Therefore, 30/(15+x) + 30/(15-x) = 9/2

900/(225-x^2) = 9/2

9x^2 = 225

x^2 = 25

x = 5

Answer 2

Let, the speed of the stream be x km/hr

Speed of boat in still water =20 km/hr

∴Speed of boat with downstream 20+x km/hr

∴ Speed of boat with upstream 20−x km/hr

As per given condition

20−x48−20+x48=1

⟹48[20−x1−20+x1]=1

⟹[(20−x)(20+x)20+x−20+x]=481

⟹400−x22x=481

⟹96x=400−x2

⟹x2+96x−400=0

⟹x2+100x−4x−400

⟹x(x+100)−4(x+100)=0

⟹(x−4)(x+100)=0

Either, x=4 or x=−100

∵ Speed cannot be negative ∴x=4 km/hr is considered.

∴ the speed of the stream =4 km/hr