Question

A stream flows at a rate of 4 mph. a boat travels 70 miles downstream and returns in a total time of 6 hr. what is the speed of the boat in still water?

Answer 1

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


`x= \frac{-b+/- \sqrt{b^(2)-4ac} }{2a} \\ \\ x= \frac{70+/- \sqrt{70^(2)+4*3*32} }{2*3} = (70+/- √(5284) )/(6)= (70+/- √(5284) )/(6)`

x=24(mi/h),
We need only positive value.