A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

Or

Find the roots of the equation

Let the speed of the stream be x km/hr

Speed of the boat upstream =( 20 – x )km/hr

Speed of the boat downstream =( 20 + x)km/hr

Distance =48km (given).

me taken in journey upstream =. hr

Time taken in journey upstream =hr

Time(upstream)-Time(downstream) =1hr (given)

⇒

⇒

⇒ 96x=(20-x)(20 + x)

⇒ 96x=400-x²

⇒ x² + 96x-400=0

⇒ x² + 100x-4x-400=0

⇒ x(x + 100)-4(x + 100)=0

⇒ (x-4)(x + 100)=0

Possible values of x are x=4 and x=-100

Rejecting the negative value of x,

∴ Speed of stream =4km/hr

Or

(taking LCM)

⇒

⇒ -30=(x + 4)(x-7)

⇒ -30=x²-3x-28

⇒ X²-3x + 2=0

⇒ X²-2x-x + 2=0

⇒ x(x-2)-1(x-2)=0

⇒ (x-1)(x-2)=0

x=-1 or x=-2