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A fish swims upstream a distance of 16 miles in a river with a current of 3 miles per hour. The fish returns swimming
downstream the same distance. The roundtrip up and down the river takes the fish 4 hours. Assuming that the fish
swims at a constant speed in still water, what is the fish's speed in still water?

Sagot :

Answer:

9 mph = the speed in still water

Step-by-step explanation:

Let r = the speed in still water

Then the speed going down stream is r + 3

and the speed going upstream is r - 3

d = rt   or t = d/r

time going downstream is 16/(r + 3) and time going upstream is 16/(r - 3)

The total time was 4 hours, so

[tex]\frac{16}{r + 3} + \frac{16}{r - 3} = 4[/tex]   Multiply thru the equation by (r + 3)(r - 3)

Then 16(r - 3) + 16(r + 3) = 4(r + 3)(r - 3)

         16r - 48 + 16r + 48 = [tex]4r^{2}[/tex] - 36

         [tex]4r^{2}[/tex] - 36 = 32r

         [tex]4r^{2}[/tex] - 32r - 36 = 0

         [tex]4(r^{2} - 8r - 9) = 0[/tex]

         4(r - 9)(r + 1) = 0

             r = 9  or -1

But a rate of speed cannot be negative, so x ≠ -1

So, r = 9 mph = the speed in still water

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