Question

a motor boat speed 20 km per h in still water takes one hour more to go 48 upstream than to return downstream to same spot find the speed of stream​

Answer 1

Answer:

The “speed of the given stream” is 4km/hr.

Solution:

Now let us take the speed of the stream as x

Therefore, the speed of boat upstream is equal to \frac{48}{20-x} and the speed of the boat downstream is \frac{48}{20+x}.

Now as to find the value of the speed of the stream we subtract the speed of downstream from upstream we get:

\frac{48}{20-x}-\frac{48}{20+x}=1

48(2 x)=400-x^{2}

x^{2}+96 x-400=0

x(x+100)-4(x+100)

x=4,-100

Now as we can see that after solving the equation we get two values one is 4 and the other one is -100. Now the value of speed can never be negative therefore x = 4 km/hr is the correct value for the speed of the stream.

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