Question

Boat takes 3 hours to go 6 miles upstream. it can go 18 miles downstream in the same time. find the rate of the current and the rate of the boat in still water

Answer 1

Find the MPH of the boat when it goes upstream... 3h / 6m = 1h / 2m
So, 2mph
Speed of the boat - current = 2mph - > x - y = 2
Find the MPH of the boat going downstream... 3h / 18m = 1h / 6m
So, 6mph
x + y = 6
We now have a system of equation, let's solve it!

x - y = 2 -> x = y + 2
x + y = 6  - >  (y + 2) + y = 6  ->  2y + 2 = 6   ->   2y = 4    ->   y = 2
This is the speed of the current!
Subtitute y = 2 in the first equation:
x - 2 = 2
x = 4
This is the speed of the boat
Rate of the current = 2mph
Rate of the boat in still water = 4mph