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
.
Upstream speed would be
.
We have been given that a boat traveled 96 miles downstream and back. The trip downstream took 4 hours.
![\text{Rate}=\frac{\text{Distance}}{\text{Time}}](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3D%5Cfrac%7B%5Ctext%7BDistance%7D%7D%7B%5Ctext%7BTime%7D%7D)
![x+y=\frac{96}{4}...(1)](https://tex.z-dn.net/?f=x%2By%3D%5Cfrac%7B96%7D%7B4%7D...%281%29)
![x+y=24...(1)](https://tex.z-dn.net/?f=x%2By%3D24...%281%29)
We are also told that the trip back took 12 hours. We can represent this information in an equation as:
![x-y=\frac{96}{12}...(2)](https://tex.z-dn.net/?f=x-y%3D%5Cfrac%7B96%7D%7B12%7D...%282%29)
![x-y=8...(2)](https://tex.z-dn.net/?f=x-y%3D8...%282%29)
Upon adding equation (1) and equation (2), we will get:
![x+x+y-y=24+8](https://tex.z-dn.net/?f=x%2Bx%2By-y%3D24%2B8)
![2x=32](https://tex.z-dn.net/?f=2x%3D32)
![\frac{2x}{2}=\frac{32}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B32%7D%7B2%7D)
![x=16](https://tex.z-dn.net/?f=x%3D16)
Therefore, the speed of boat in the still water is 16 miles per hour.
Upon substituting
in equation (1), we will get:
![16+y=24](https://tex.z-dn.net/?f=16%2By%3D24)
![16-16+y=24-16](https://tex.z-dn.net/?f=16-16%2By%3D24-16)
![y=8](https://tex.z-dn.net/?f=y%3D8)
Therefore, the speed of the current is 8 miles per hour.