Question

a motorboat whose speed 20km ler hr in still water take 1 hr more too go 48 km upstream that to return downstream to the same spot .find the speed of the stream​

Answer 1

Answer:

4 km/hr

Step-by-step explanation:

speed of boat = 20 km/h

let the speed of stream = x km/h

speed of the boat upstream = 20-x km/h

speed of the boat downstream = 20+x km/h

distance covered = 48 km

time take going upstream = 48/(20-x) hrs

time taken going downstream = 48/(20+x) hrs

48/(20-x) - 48/(20+x) = 1   ................given

taking LCM, we get

(48(20+x) - 48(20-x))/(400-x²) = 1

960 + 48x - 960 + 48x = 400-x²

96x + x² - 400 = 0

x² + 100x - 4x -400 = 0

x(x+100)-4(x+100) = 0

(x-4)(x+100)=0

x=4 x cannot be equal to -100, because speed is always positive

hence speed of the stream is 4km/hr

Answer 2

Answer:

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