Question

$\huge \fbox \blue{❥Question}$

A race-boat covers a distance of 66 km downstream in 110 minutes. It covers this distance in 120 minutes. The speed of the boat is still water is 34.5 km/h. Find the speed of the stream.




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Answer 1

$\huge\mathfrak{\underline{\underline{\red{Answer}}}}$

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

when the racing boat is going downstream it's speed is (34.5+x)km/hr and while going upstream it's speed is (34.5-x)km/hr

$\sf \frac{66}{(34.5 + x)} = \frac{110}{60} \: or \\ \sf110(34.5 + x) = 66 \times 60 \: \: or \\ \sf \: (34.5 + x) = 66 \times \frac{60}{110} = 36 \: or \\ \sf \: x = 36 - 34.5 = 1.5km/</p><p>hr$

check : 66/(34.5-x)=66/(34.5-1.5)=66/33 = 2 hours

the stream flow is 1.5km/hr

Answer 2

$\huge\mathfrak\red{♡answer♡} \\ \\ \: \: \: \: ✍$

$⇒ \: distnace \: of \: race \: boat \: \\ downstream = 66km$

$⇒time \: taken \: downstream = 110 \\ minutes = \frac{110}{60} hr$

$⇒time \: taken \: upstream \: 1 = 120 \\ minutes = \frac{120}{60} hr$

$⇒speed \: of \: boat \: in \: still \: water \: \\ = 34.5km \hr$

$⇒ \: let \: the \: speed \: of \\ \: the \: stream \: of \: the \\ stream \: flow \: be \: x \: km (hr.$

$⇒when \: the \: racing \: boat \: is \: going \: \\ downstream \: its \\ \: speed \: is \: (34.5 + x) \: km (hr.$

$and \: while \: going \: upstream \: its \: \\ speed \: is \: (34.5 - x)km(hr.$

$⇒using \: time = \frac{distance}{speed} \: \\ we \: have \: for \:$

$downstream \: \\ \frac{66}{(34.5 + x)} = \frac{110}{60}$

$\huge\mathfrak\red{}$

$➵ 110(34.5 + x) = 66 + 60 \\ \\ ➵ \: (34.5 + x) = (66 \times 60) \\ 110 = 36$

$➵ \: x = 36 - 34.5 = 1.5km \hr.$

Hence the stream flow is 1.5 km/hr

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