Respuesta :
Answer:
Speed of boat is still water: 16 miles per hour.
Speed of current: 8 miles per hour.
Step-by-step explanation:
Let x represent speed of boat in still water and y represent speed of current.
Downstream speed would be [tex]x+y[/tex].
Upstream speed would be [tex]x-y[/tex].
We have been given that a boat traveled 96 miles downstream and back. The trip downstream took 4 hours.
[tex]\text{Rate}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]x+y=\frac{96}{4}...(1)[/tex]
[tex]x+y=24...(1)[/tex]
We are also told that the trip back took 12 hours. We can represent this information in an equation as:
[tex]x-y=\frac{96}{12}...(2)[/tex]
[tex]x-y=8...(2)[/tex]
Upon adding equation (1) and equation (2), we will get:
[tex]x+x+y-y=24+8[/tex]
[tex]2x=32[/tex]
[tex]\frac{2x}{2}=\frac{32}{2}[/tex]
[tex]x=16[/tex]
Therefore, the speed of boat in the still water is 16 miles per hour.
Upon substituting [tex]x=16[/tex] in equation (1), we will get:
[tex]16+y=24[/tex]
[tex]16-16+y=24-16[/tex]
[tex]y=8[/tex]
Therefore, the speed of the current is 8 miles per hour.
