Question

pratik travels by boat 36km downstream and back in 8 hours. if tge speed of a boat in still water is 12km/h, find the speed of water current.

Answer 1

ANSWER:

Let the speed of the river current=x km/hr.

Speed of boat in still water=12 km/hr.

Speed of boat up the river

=(12-x) km/hr.

Speed of boat under the river =(12+x)km/hr.

$\\ time = \frac{distance}{speed}$

Time taken by the boat to travel 36 km down the river

$\\ = (\frac{36}{12 + x}) \: hrs$

As per the given condition,

$\\ \frac{36}{12 + x} + \frac{36}{12 - x} = 8 \\ \\ 36( \frac{1}{12 + x} + \frac{1}{12 - x} ) = 8 \\ \\ \frac{12 - x + 12 + x}{(12 + x)(12 - x)} = \frac{8}{36} \\ \\ \frac{24}{144 - {x}^{2} } = \frac{2}{9} \\ \\ 108 = 144 - {x}^{2} \\ \\ {x}^{2} = 144 - 108 \\ \\ {x}^{2} = 36 \\ \\ \sqrt{ {x}^{2} } = \sqrt{36}......(taking \: square \: roots \:on \: both \: sides) \\ \\ x \: = \: ± \: 6</p><p></p><p></p><p></p><p></p><p></p><p>$

x≠-6 as speed cannot be negative.

x=6.

Therefore,

The speed of the river current is 6 km/hr.