Question

The speed of the boat in still water is 15 km/h. It can go 30 km upstream and return downstream
to the original point in 4 h and 30 min. Find the speed of stream .

Answer 1

$\huge\mathfrak\red{Answer}$

Given, Speed of the 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 taken for upstream

$T_{1} = \frac{30}{15 - x}$

Time taken for downstream

$T_{2} = \frac{30}{15 + x}$

Given,

$T_{1} + T_{2} = \frac{9}{2} \\ = \frac{30}{15 - x} + \frac{30}{15 + x} = \frac{9}{2} \\ = 30\Bigg( \frac{1}{15 - x} + \frac{1}{15 + x} \Bigg) = \frac{9}{2} \\ = 30\Bigg( \frac{15 + x \div 15 - x}{(15 - x)(15 + x)} \Bigg) = \frac{9}{2} \\ = \frac{30 \times 30}{225 - {x}^{2} } = \frac{9}{2} \\ = \frac{100}{225 - {x}^{2} } = \frac{1}{2} \\ = 225 - {x}^{2} = 200 \\ = {x}^{2} = 25 \\ x = \sqrt{25} = 5$

Speed of the stream = 5km/hr.