Question

Question23: a motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Answer: Speed of stream be x

Velocity in Upstream be x-24

Velocity in downstream be x+24

So According to question

Time travel in Downstream + 1 hour = Time travel in Upstream

$\frac{32}{x+24}  + 1 = \frac{32}{x-24}$

So It form quadratic equation

by solving this equation we get

x= 8 or -72

So Speed of stream be 8 Km/hr (as -72 is negative)

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