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

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