Answer:
- boat: 52 km/h
- current: 14 km/h
Explanation:
You want to know the speeds of boat and current given a 5-hour trip and an upstream distance of 190 km and a downstream distance of 330 km.
Upstream speed
Let b and c represent the speeds of boat and current, respectively. The speed upstream is ...
speed = distance/time
b -c = 190/5 = 38 . . . . . km/h
Downstream speed
Similarly, the downstream speed is ...
b +c = 330/5 = 66 . . . . . km/h
Boat speed
Adding the two equations gives ...
(b -c) +(b +c) = (38) +(66)
2b = 104
b = 52 . . . . . km/h
Current speed
Subtracting the first equation from the second gives ...
(b +c) -(b -c) = (66) -(38)
2c = 28
c = 14 . . . . . km/h
The speed of the boat in still water is 52 km/h; the speed of the current is 14 km/h.
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Additional comment
On planet Earth, you might have trouble finding a river 330 km long that has a current of 14 km/h over that length. Most rivers decline in speed to about 6 km/h after the initial plunge from the hills where they are born.