Question

a motor boat whose speed is 20 km/hr in still water, takes 1hour more to go 48 km up stteam than to return down stream to the samr spot. find the speed of the stream​

Answer 1

Answer:

Step-by-step explanation:

Question :-

A motor boat, whose speed is 20 km/hr 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.

Solution :-

Let the speed of the stream be x km/hr

Therefore,

Speed of boat in downstream = 20 + x km/hr

Speed of boat in upstream = 20 - x km/hr

According to the Question,

$\bf\implies \dfrac{48}{20-x}-\dfrac{48}{20+x}=1$

$\sf\implies 48(\dfrac{1}{20-x}-\dfrac{1}{20+x})=1$

$\sf\implies \dfrac{20+x-20+x}{(20-x)(20+x)}=\dfrac{1}{48}$

$\sf\implies \dfrac{2x}{400-x^2}=\dfrac{1}{48}$

$\bf\implies x^{2}+96x-400=0$

$\sf\implies x^{2}+100x-4x-400=0$

$\sf\implies x(x+100)-4(x+100)=0$

$\sf\implies (x-4)(x+100)$

$\bf\implies x=4,-100 (Speed \: cannot \: be \: negative)$

$\bf So, \: x=4 \: km/h$

Hence, the speed of the stream​ is 4 km/h.

Answer 2

Answer:

$\underline{\boxed{\red{\bf Speed \: of \: stream = 4 \: km/hr}}}$

Step-by-step explanation:

Given that :

• Speed of motor boat in still water = 20 km/hr.

To find :

• Speed of the stream.

Solution :

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

So,

Speed of motor boat in downstream = speed in still water + speed of stream.

⇒ Speed of boat in downstream = (20 + x) km/hr.

Speed of motor boat in upstream = speed in still water - speed of stream.

⇒ Speed of boat in upstream = (20 - x) km/hr.

According to the problem given,

$\bf \longrightarrow \dfrac{48}{20-x}-\dfrac{48 +x}{20+x}=1$

Taking LCM,

$\longrightarrow \bf \dfrac{48(20+x)-48(20-x)}{(20-x)(20+x)} \\\\\longrightarrow \bf 48(\frac{20+x - 20+x}{(20-x)(20+x)}) = 1 \\\\\longrightarrow \bf \frac{2x}{400-x^2}=\frac{1}{48}$

On cross-multiplying,

$\longrightarrow \bf 400 - x^2 = 96x \\\\\longrightarrow \bf x^2 +96x-400 = 0 \\\\\longrightarrow \bf x^2 + 100x - 4x - 400 = 0\\\\\longrightarrow \bf x(x+100) - 4(x + 100)=0\\\\\longrightarrow \bf (x+100)(x-4)=0\\\\\implies \: \boxed{\bf \therefore x = - 100 \: or \: x = 4}$

Since, speed cannot be negative.

★ $\boxed{\bf x = 4 \: km/hr}$

Hence, the speed of the stream is 4 km/hr.