A motor boat traveled 87.75 miles down a river in 13.5 hours but going back upstream it took 19.5 hours due to the current. Find the rate of the motor boat in still water and the rate of the current.
boatspeed = v
current sped = c
downstream velocity = v+c
so
(v+c) (13.5) = 87.75
(v-c) (19.5) = 87.75
13.5 v + 13.5 c = 87.75
19.5 v - 19.5 c = 87.75
19.5 / 13.5 = 1.444 so multiply first equation by that
19.5 v + 19.5 c = 126.75
19.5 v - 19.5 c = 87.75
------------------------------- subtract
39 c = 39
c = 1
now go back and get v