x - speed of the boat in still water
(x+4) - speed of the boat downstream
(x-4) - speed of the boat upstream
70/(x+4)- time of the traveling downstream
70/(x-4) - time of the traveling upstream
70/(x+4) + 70/(x-4) = 6
(70x-280+70x+280)/(x-4)(x+4) = 6(x-4)(x+4) /(x-4)(x+4)
140x = 6(x²-16)
6x²-140x-96 =0
3x² -70x-32=0
[tex]x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
\\ \\ x= \frac{70+/- \sqrt{70^{2}+4*3*32} }{2*3} = \frac{70+/- \sqrt{5284} }{6}= \frac{70+/- \sqrt{5284} }{6}
[/tex]
x=24(mi/h),
We need only positive value.
