Answer:
8 km/h
Step-by-step explanation:
Let x represent the speed of the stream in km/h. The relation between time, sped, and distance is ...
time = distance/speed
Upstream, the speed of the current is subtracted from the speed of the boat in still water to obtain the speed of progress relative to the bank. Downstream, the current speed adds to the boat speed. The difference in travel times in hours can be written as ...
32/(24-x) -32/(24+x) = 1
Multiplying by the product of denominators, we have ...
32(24+x) -32(24-x) = (24+x)(24-x)
64x = 24^2 -x^2
x^2 +64x +32^2 = 24^2 +32^2 . . . . . add x^2 and complete the square
(x +32)^2 = 40^2 . . . . . . . . write as squares
x = -32 +40 . . . . . . . . . . . . . take the positive square root
x = 8
The speed of the current is 8 km/h.
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I find a graphing calculator to be a quick and easy way to solve problems like this.
