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64 A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current. Knowing that the speed of the boat in still water is 9 km/hour, find the speed of the river’s current.

Respuesta :

sqdancefan
Let c represent the speed of the current.

time = distance / speed

total time = time going upriver + time going downriver
2 2/3 = 6/(9 -c) + 6/c
(8/3)(c)(9 -c) = 6c +6(9 -c)
(8/3)c^2 -24c +54 = 0
c = (24 ± √((-24)^2 -4(8/3)(54)))/(2*8/3)
.. = (3/16)(24)
c = 4.5

The speed of the river's current is 4.5 km/h.
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