- #1

mirs

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## Homework Statement

A biologist determines experimentally that the number of calories burned by a salmon swimming a distance d in miles upstream against a current v0 in miles per hour is given by

Energy = kdv^5/v − v0

where v is the salmon’s swimming speed relative to the water it is in. This means that the salmon’s progress upstream is at the rate of v − v0 miles per hour, so that the distance d is covered in a time of

t=d/v − v0

If v0 = 2 mph and d = 20 miles, and the salmon, being smart, swims so as to minimize the calories burned, how many hours will it take to complete the journey?

## Homework Equations

Requires derivatives

## The Attempt at a Solution

I really just don't understand where to start. I subbed t into the equation and ended up with ktv^5/v-v0, took the derivative of that with respect to t and got 5kv^4 but I have no idea what I really don't know where to go from there.