- #1

Gib Z

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Question:

The Current in a river moves at a speed of 4km/h. A boat travels 32km upriver and 32km downriver in a total time of 6 hours. What is the speed of the boat in still water?

Relevant Equations:

[tex]Speed=\frac{Distance}{Time}[/tex]

Attempt:

I don't know whats wrong! This is meant to be a simple question, maybe my brains farting...

Let x be the speed in still water.

On its 32km upriver with the current, its speed is x+4 km/h,

on its 32km down its speed is x-4 km/h.

Let the time it took for the way upriver be t_1, and down t_2,

then on its way up, by s=d/t,

[tex]x+4=\frac{32}{t_1}[/tex]

Down:[tex]x-4=\frac{32}{t_2}[/tex]

Solving for the times, and adding them,

we get [tex]\frac{32}{x+4} + \frac{32}{x-4} = 6[/tex] since t_1 + t_2 must equal 6 hours, as given.

I multiplyed everything by x^2 - 16, expanded a simplyfied the quadratic equation, i end up with [tex]3x^2 - 32x -48=0[/tex] which i know isnt right >.< Help