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?

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

  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 = - 36

          - 36 = 32r

          - 32r - 36 = 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

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).