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Karina rows a boat downstream for 66 miles. The return trip upstream took 16 hours longer. If the current flows at 4 mph, how fast does Karina row in still water?

Respuesta :

opudodennis

Answer:

7 mph

Step-by-step explanation:

Let x be the speed in still water hence

Time to move downstream will be [tex]\frac {66}{x+4}[/tex]

Time to move upstream will be [tex]\frac {66}{x-4}[/tex]

Difference will be

[tex]\frac {66}{x-4}-\frac {66}{x+4}=16[/tex]

[tex]66(x+4)-66(x-4)= 16(x^{2}-16)[/tex]

[tex]66x+264-66x+264=16x^{2}-256[/tex]

[tex]16x^{2}-256-528=0[/tex]

[tex]x^{2}-16-33=0[/tex]

[tex]x^{2}=49[/tex]

x=7

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