Question

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★★ A MOTORBOAT CAN TRAVEL 30 KM UPSTREAM AND 28 KM DOWNSTREAM IN 7 H . IT CAN TRAVEL 21 KM UPSTREAM AND RETURN IN 5 H. FIND THE SPEED OF THE BOAT IN STILL WATER AND THE SPEED OF THE STREAM..

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Answer 1

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→ Let speed of Boat in still water = x km/h

→ Let speed of stream = y km/h

ATC - 1

$\frac{30}{x - y} + \frac{28}{x + y} = 7$

Let,

$\frac{1}{x - y} = a \:( and )\: \frac{1}{x + y} = b$

So,

$30a + 28y = 7 \: \: \: - - - - - -(1)$

ATC - 2

$\frac{21}{x - y} + \frac{21}{x + y} = 5$

$21a + 21b = 5 \: \: \: - - - - - (2)$

Multiply by 21 to eqñ ( 1 ) and 28 to eqñ ( 2 ) .

On solving them we get,

630a + 588b = 147

588a + 588b = 140

__________

42a = 7

$a \: = \frac{7}{42} \\ a = \frac{1}{6}$

Put a in ( 1 )

$\frac{30}{6} + 28b = 7 \\ 5 + 28b = 7 \\ 28b = 2 \\ b = \frac{1}{14}$

But,

$\frac{1}{x - y} = a \\ x - y = 6 \: \: \: \: \: \: \: \: \: \: \: - - - - - (3)$

$\frac{1}{x + y} = \frac{1}{14} \\ x + y = 14 \: \: \: \: - - - - - - - (4)$

By eqñ ( 3 ) and ( 4 )

x - y = 6

x + y = 14

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2x = 20

x = 10

put x in ( 1 )

10 - y = 6

- y = -4

y = 4

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Answer 2

Something for you read it carefully I wrote it for you pls read properly