Question

 A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.


It's a question of arithmetic progression
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Answer 1

$\rightarrow\small\tt \purple{Given}$

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$\circ\small \tt{ \: Distance = 24 km}$

$\circ\small \tt{ \: Speed = \: 18km \: per \: hr }$

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$\circ\small\tt{ \: Speed \: of \: upstream = 18 - x}$

$\circ\small\tt{ \: Speed \: of \: downstream = 18 + x}$

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$\circ\tt \purple{ \: Time \: = \frac{Distance}{Speed} }$

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$\purple\rightarrow\small\tt{ATQ}$

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$\rightarrow\small\tt \purple{Equation \: Becomes}$

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$\rightarrow\tt \purple{ \frac{24}{18 - x} = } \tt{ \frac{24}{18 + x} + 1}$

$\rightarrow\tt \purple{ \frac{24}{18 - x} = } \tt{ \frac{1(24) + 1(18 - x)}{18 + x} }$

$\rightarrow\tt \purple{ \frac{24}{18 - x} = } \tt{ \frac{24 + 18 + x}{18 + x} }$

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$\purple \rightarrow\small\tt{Do}\small\tt\purple{ \:Cross \: Multiplication}$

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$\rightarrow \small\tt \purple{ 24(18 + x) = } \tt{(24 + 18 + x)(18 - x) }$

$\rightarrow \small\tt \purple{ 432 + 24x = } \tt{24(18 - x) + 18 (18 - x)+ x(18 - x) }$

$\rightarrow \small\tt \purple{ 432 + 24x = } \tt{432 - 24x + 324 - 18x+ 18x - {x}^{2} }$

$\rightarrow \small\tt \purple{ \cancel{432} - \cancel{ 432}+ 24x + 24x = } \tt{ 324 - \cancel{18x}+ \cancel{18x} - {x}^{2} }$

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$\rightarrow \small\tt \purple{ {x}^{2} + 48x - 324 = } \tt{ 0}$

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$\purple \rightarrow\small\tt{By}\small\tt\purple{ \: Factorisation \: Method}$

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$\rightarrow \small\tt \purple{ {x}^{2} + 54x - 6x- 324 = } \tt{ 0}$

$\rightarrow \small\tt \purple{ x(x + 54) - 6(x + 54) = } \tt{ 0}$

$\rightarrow \small\tt \purple{ (x + 54) (x- 6) = } \tt{ 0}$

$\rightarrow \small\tt \purple{ x + 54 = } \tt{ 0}$

$\boxed{\rightarrow \small\tt \purple{ x = } \tt{ ( - 54)}}$

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$\rightarrow \small\tt \purple{ x- 6 = } \tt{ 0}$

$\boxed{\rightarrow \small\tt \purple{ x = } \tt{ 6}}$

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x value can't be negative so that's why we take x = 6

Answer 2

Answer:

Just take the positive value 6