Optimization problem that makes no sense

[Burjam]

Homework Statement

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is $675 per hour. At what speed should it travel so as to minimize the cost per mile traveled?

Homework Equations

N/A

The Attempt at a Solution

I'm having trouble setting up functions to solve this problem. I could do it if I just had some solid functions to work with. The thing that's really getting me is the wording.

The problem states:

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour.

Last time I checked, 10^3 is 1000. What's going on here?

 

[Mark44]

Homework Statement

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is $675 per hour. At what speed should it travel so as to minimize the cost per mile traveled?

Homework Equations

N/A

The Attempt at a Solution

I'm having trouble setting up functions to solve this problem. I could do it if I just had some solid functions to work with. The thing that's really getting me is the wording.

The problem states:

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour.

Last time I checked, 10^3 is 1000. What's going on here?

It doesn't say that the cost is the cube of the speed, just that the cost is proportional to the cube of the speed. For example, if the boat's speed was increased to 20 mph, it would use $800 of fuel per hour.

 

[Burjam]

Ok did it. I got 15mph which is what the back of the book says. Thanks