A motorboat travels 96km in three hours going upstream it travels 160km going downstream in the same amount of time. what is the rate of the boat in still water

The speed of motorboat in still water = 42.67 km / h

Explanation:

Let speed of motorboat = u

     speed of current = v

Then upstream speed = u - v

Negative  sign is due to that the current and motorboat directions are opposite.

And downstream speed = u + v

Distance traveled by motorboat in upstream = 96 km

Time taken = 3 hours

Then upstream speed (u - v) = = 32 km / h ---------------- (1)

Distance traveled by motorboat in downstream = 160 km

Time taken = 3 hours

Downstream speed (u - v) = km / h =  53.34 km / h -------------------------- (2)

By adding equations (1) & (2), we get

⇒ 2 u = 32 + 53.34

⇒ 2 u = 85.34

⇒ u =

⇒ u = 42.67 km / h

Thus the speed of motorboat in still water = 42.67 km / h