Answer:
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) = [tex]\frac{96}{3}[/tex] = 32 km / h ---------------- (1)
Distance traveled by motorboat in downstream = 160 km
Time taken = 3 hours
Downstream speed (u - v) = [tex]\frac{160}{3}[/tex] km / h = 53.34 km / h -------------------------- (2)
By adding equations (1) & (2), we get
⇒ 2 u = 32 + 53.34
⇒ 2 u = 85.34
⇒ u = [tex]\frac{85.34}{2}[/tex]
⇒ u = 42.67 km / h
Thus the speed of motorboat in still water = 42.67 km / h
