A motorboat travels 105 kilometers in 3 hours going upstream. It travels 165 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Rate in still water = 45 km/h

Rate of the current = 10 km/h.

Step-by-step explanation:

Let the rate of the current be x and rate in still water be y.

So the rate of the boat upstream is y - x and the rate downstream = x + y.

Rate upstream = distance / time

y - x = 105/3 = 35 (1)

Rate downstream:

y + x = 165/3 = 55 (2)

Adding (1) + (2):

2y = 90

y = 45 km/h.

Using equation (1):

45 - x = 35

x = 45-35 = 10 km/h.