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A boat goes 12 km downstream and 26 km upstream in 8 hours.It can go 16 km upstream and...

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topalle | Student, Grade 10 | Honors

Posted May 19, 2012 at 8:49 AM via web

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A boat goes 12 km downstream and 26 km upstream in 8 hours.It can go 16 km upstream and 32 km downstream in the same time. Find the speed of boat in still water and the speed of current.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 19, 2012 at 1:00 PM (Answer #1)

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Let the speed of the boat upstream be X and the speed of the boat downstream be Y.

The boat goes 12 km downstream and 26 km upstream in 8 hours.

=> 12/Y + 26/X = 8

It can go 16 km upstream and 32km downstream in the same time.

=> 16/X + 32/Y = 8

12/Y + 26/X = 16/X + 32/Y

=> 20/Y = 10/X

=> 2X = Y

12/Y + 26/X = 8

=> 12/2X + 26/X = 8

=> 32 = 8X

=> X = 4

Y = 8

When the boat goes downstream the speed of the current is added to the speed of the boat in still water. When it goes upstream the speed of the current is subtracted from the speed of the boat in still water.

B - C = 8 and B + C = 4

2B = 12

=> B = 6

and C = 2

The speed of the boat in still water is 6 km/h and the speed of the current is 2 km/h

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popatlal | Student, Grade 9 | Honors

Posted May 19, 2012 at 9:30 AM (Answer #2)

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TRY USING SIMULTANEOS EQUATIONS....

x=STILL WATER & y = CURRENT

y =7 AND x=5

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