# Thread: Pre-Calculus Word Problems Help

1. ## Pre-Calculus Word Problems Help

So, my teacher recently assigned a few problems for homework that I am completely clueless about.

I was wondering if somebody could assist me in at least outlining the steps needed to solve the following problem:

The cost of renting a large boat is 30 dollars per hour plus a usage fee roughly equivalent to $\displaystyle x^3$ cents per hour when the boat is operated at a speed of x $\displaystyle km/h$. Express the cost C (in cents per kilometer) as a function of x.
Thanks

$\displaystyle distance = rate \times time$ or $\displaystyle d=r \times t$.

So if you go $\displaystyle d$ km for $\displaystyle t$ hours, then $\displaystyle \frac{d}{t}=r$ km per hour.

$\displaystyle \left(\frac{d}{t}\right)^3\times t + 3000\times t$ gives the total cost (in cents) combining the hourly and usage fees, so $\displaystyle \frac{\left(\frac{d}{t}\right)^3\times t + 3000\times t}{d}$ is the total cost per km.

Since you want to get the cents per $\displaystyle 1$ km at $\displaystyle x$ km per hour, use the simple distance formula to arrive at: $\displaystyle f(x)=\left(x^3+3000\right)\times \frac{1}{x}$.

I'm curious to see how others would solve this problem.

3. You're welcome, Marko. For future reference, it's better if you don't edit your post to remove the original problem statement. Instead, simply post a new reply. This way others browsing the thread in the future will be able to benefit from it.