# Thread: trouble setting up derivative word problem

1. ## trouble setting up derivative word problem

I know I should be taking the derivative of this equation to get the minimum but I'm having trouble setting up the equation of this word problem to begin with:

The distance by bus from NY to Boston is 225 miles. The bus driver gets paid \$12.50 per hour, while the other costs of running the bus at a steady speed of x miles per hour amount to 90+0.5x cents per mile. The minimum and maximum legal speeds on the bus route are 40 and 55 miles per hour. At what steady speed should the be driven to minimize the total cost?

Thanks

2. ## Re: trouble setting up derivative word problem

I suspect the part that's giving you trouble is figuring out how the bus drivers wage depends on x. Use the formula distance=rate x time.
NY to Boston is 225 miles, rate is x. So time = (225 miles)/x(miles/hour) = 225/x hours.

The bus driver's total wage from the trip is
12.50(dollars)(time)/hour = 12.50(dollars)(225/x)(hours)/hour = 12.50*225/x dollars.

Make sure your final equation has the right units of currency (right now there are both dollars and cents).