Question

The speed of the boat in still water in 11 km /hr . it can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the boat of the stream ?​

Answer 1

$\small\green {Question:-}$

The speed of the boat in still water in 11 km /hr . it can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the boat of the stream ?

$\huge \orange{ \underline \red{ \underline \purple{Solution:}}}$

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

Given, speed of the boat in still water = 11 km/hr

Speed of the boat upstream = Speed of the boat in still water – Speed of the stream

∴ Speed of the boat upstream = (11 – x) km/hr

Speed of the boat downstream = Speed of the boat in still water + Speed of the stream

∴ Speed of the boat downstream = (11 + x) km/hr

Distance covered by the boat upstream = Distance covered by the boat downstream = 12 km

Given, Time for upstream journey + Time for downstream journey = 2 hr 45 min

$\frac{distance \: of \: covered \: upstream}{speed \: of \: the \: boat \: upstream} + \frac{distance \: covered \: dowmstream}{speed \: of \: the \: boat \: downstream} = 2hr + \frac{45}{60} hr = \frac{11}{4} hr$

$\frac{12km}{(11 - x)km \: hr} + \frac{12km}{(11 + x)km \: hr} = \frac{11}{4} hr$

$\frac{12}{11 - x} + \frac{12}{11 + x} = \frac{11}{4}$

$\frac{12(11 + x) + 12(11 - x)}{(11 - x)(11 + x)} = \frac{11}{4}$

$\frac{132 + 12x + 132 - 12x}{12 - {x}^{2} } = \frac{11}{4}$

$\frac{264}{121 - {x}^{2} } = \frac{11}{4}$

$96 = 121 - {x}^{2}$

${x}^{2} = 121 - 96 = 25$

$x = + 5$

$x = 5(x \: cannot \: be \: negative)$

Thus, the speed of the stream is 5 km/h