Question

It takes a total of 15 hours for a boat to reach its destination in calm waters and return to its starting point from there. The same journey requires 16 hours if the river flows. The difference between the speed of the boat and the river is 15 km. / Hour. Find the speed of river flow.​

Answer 1

Given

Speed of boat in still water = 15km/hr

Let x be speed of the stream in km/hr

Speed of the boat upstream = 15 - x

Speed of the boat down stream = 15 + x

$time \: take \: for \: upstream \: t1 = \frac{30}{15 - x}$

$time \: taken \: for \: down \: stream \: t2 = \frac{30}{15 - x}$

$given \: t1 + t2 = \frac{9}{2}$

$= \frac{30}{15 - x} + \frac{30}{15 - x} = \frac{9}{2}$

$= 30( \frac{1}{15 - x} + \frac{1}{15 - x} ) = \frac{9}{2}$

$= 30( \frac{15 + x \div 15 - x}{(15 - x)(15 + x)} ) = \frac{9}{2}$

$\frac{30 \times 30}{225 - {x}^{2} } = \frac{1}{2}$

$\frac{100}{225 - {x}^{2} } = \frac{1}{2}$

$225 - {x}^{2} = 200$

${x}^{2} = 25$

$x = 5$

$x = 5km$

speed of the stream 5km/hr