Question

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?

Answer 1

9 mph = the speed in still water

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

`(16)/(r + 3) + (16)/(r - 3) = 4` 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 =
`4r^(2)` - 36

`4r^(2)` - 36 = 32r

`4r^(2)` - 32r - 36 = 0

`4(r^(2) - 8r - 9) = 0`

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