# Math Help - Calculus word problem

1. ## Calculus word problem

A small buisness uses a minivan to make deliverys. The cost per hour for fuel is F=(v^2)/360, where v is the speed of the minivan (in miles per hour). The driver is paid $10 per hour. Find the speed that minimizes the cost of a 110 mile trip. ( assume there are no costs other then fuel and wages.) 2. Originally Posted by geryuu A small buisness uses a minivan to make deliverys. The cost per hour for fuel is F=(v^2)/360, where v is the speed of the minivan (in miles per hour). The driver is paid$10 per hour. Find the speed that minimizes the cost of a 110 mile trip. ( assume there are no costs other then fuel and wages.)

Rember that distance is equal to rate multiplied by time

so you your case you get

$d=vt \iff v=\frac{110}{t}$ Using this you can compute the cost of fuel per hour driven as

$F(v)=F(t)=\frac{1}{360}\left( \frac{110}{t}\right)^2$

Now just add this to his hourly wage as a function of time to get the cost function

$C(t)$

I hope this gets you started.