Question

ue slove kar dijiye proof ke sath ​

Answer 1

Answer:

Speed of the boat in still water = 8 km/hr

Step-by-step explanation:

Given that,

Speed of the river water = 4 km/hr.

Total time of the journey = 2 hr.

Solution:

Let speed of the boat in the still water be x  km/hr.

and Let, t1 and t2 be time taken for the upstream and downstream journey.

∴ Speed in the Upstream = (x - 4) km/hr.

∴ Speed in the Downstream = (x + 4) km/hr.

∵Distance traveled in upstream = 6 km.

∴Time taken in upstream (t1) = $\frac{6}{x-4}$

∴Time taken in downstream (t2) = $\frac{6}{x+4}$

∴ t1 + t2 = $\frac{6}{x-4}+\frac{6}{x+4}$

⇒2 = 6[${\frac{1}{x-4}+\frac{1}{x+4}}$]

⇒$\frac{2}{6}=[\frac{x+4+x-4}{x^{2}-16} ]$

⇒$\frac{1}{3}=[\frac{2x}{x^{2}-16} ]$

⇒$x^{2} -16=6x$

⇒$x^{2} -6x-16=0$

⇒$x^{2} -8x+2x-16=0$

⇒$x(x-8)+2(x-8)=0$

⇒$(x-8)(x+2)=0$

Either,                                                  or

x - 8 = 0                                              x + 2 = 0

⇒x = 8 km/hr                                         ⇒ x = -2 (Neglecting negative value)

                                                         [∵ Speed cannot be negative]

∴ Speed of the boat in still water = 8 km/hr.

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