Answer:
3 km/h
Explanation:
You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.
Time
The relation between time, speed, and distance is ...
time = distance / speed
If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...
36/(15 -c) = 36/c -9
Solution
Multiplying by c(15-c), we have ...
36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)
36c = 540 -36c -135c +9c² . . . . . eliminate parentheses
9c² -207c +540 = 0 . . . . . . . collect terms
c² -23c +60 = 0 . . . . . . . . divide by 9
(c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3
The speed of the current is 3 km/h.
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Additional comment
The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.
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