Amotorboat takes 3 hours to travel 108 km going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?

Recall your d = rt, distance = rate * time.

let's say the boat has a still water rate of "b", and the current has a a rate of "c", ok.... when the boat is going upstream, is not really going "b" fast, is going  slower at "b - c", due to the current going in the opposite direction.

when the boat is coming downstream, is not going "b" fast either, is going faster, is going "b + c", due to the current adding speed to it.

we know the trip up was 108 kms, thus the return trip is also 108 kms.



and surely you know how much that is.

what's the boat's speed? well, 36 + c = b.