Aboat travels 45 miles upstream (against the current) in 5 hours. the boat travels the same distance downstream in 3 hours. what is the rate of the boat in still water? what is the rate of the current?

R=rate of boat in still water
c=rate of current
d=rt
since you're given that the time it takes to travel the same distance downstream and upstream, your equation will be d_1=d_2, or rt=rt
the rate upstream is r-c and the rate downstream is r+c (because the boat's and river's rates add up)
since you know t_1 and t_1 are 5 and 3, you can now set up 2 equations
5*(r-c)=45 because (time upstream)*(rate upstream)=distance=45 miles
r-c=45/5=9
3*(r+c)=45
r+c=45/3=15
r-c=9 and r+c=15, so r=12 mi/h and c=3 mi/h
If you have any questions please ask

The solution to the system of equations (-2,2)