a boat travels 50km downstream in the same time that it take

a boat travels 50km downstream in the same time that it takes to go 30km upstream. The speed of the boat in still water is 16 km/h. Find the speed upstream.

Solution

Let s be the speed of the river.
The speed of the boat downstream is 16 + s (faster)
The speed of the boat upstream is 16 - s (slower)
D = RT
Downstream:
50 = (16 + s)t
t = 50/(16 + s)
Upstream:
30 = (16 - s)t
t = 30/(16 - s)
Since these times are the same, equate them and solve for s.
50/(16+s) = 30/(16-s)
Cross multiply:
50(16 - s) = 30(16 + s)
800 - 50s = 480 + 30s
Add 50s to both sides:
800 = 480 + 80s
Subtract 480 from both sides:
320 = 80s
Divide both sides by 80:
s = 320/80
s = 4
So the speed of the river is 4 km/h
The boat goes downstream at 16 + 4 = 20 km/h
The boat goes upstream at 16 - 4 = 12 km/h
Answer:
12 km/h upstream (against the 4 km/h current)