Respuesta :
Answer:
Speed of boat is 32 miles per hour that is 4 times speed of water (8 mph).
Step-by-step explanation:
Let x represent speed of boat in still water.
We have been given that the speed of the current was 8 mph, so the speed of boat downstream would be [tex]x+8[/tex] and speed of boat upstream would be [tex]x-8[/tex].
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
Since boat traveled a distance of 45 miles in 3 hours, so we can set an equation as:
[tex]\frac{45}{x-8}+\frac{45}{x+8}=3[/tex]
[tex]\frac{45}{x-8}*(x-8)(x+8)+\frac{45}{x+8}*(x-8)(x+8)=3(x-8)(x+8)[/tex]
[tex]45(x+8)+45(x-8)=3(x-8)(x+8)[/tex]
[tex]45x+360+45x-360=3(x^2-64)[/tex]
[tex]90x=3x^2-192[/tex]
[tex]3x^2-90x-192=0[/tex]
[tex]x^2-30x-64=0[/tex]
[tex]x^2-32x+2x-64=0[/tex]
[tex]x(x-32)+2(x-32)=0[/tex]
[tex](x-32)(x+2)=0[/tex]
[tex](x-32)=0\text{ (or) }(x+2)=0[/tex]
[tex]x=32\text{ (or) }x=-2[/tex]
Since speed cannot be negative, therefore, the speed of boat in still water is 32 miles per hour and speed of boat is 4 times speed of water.
