# Thread: 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.)
P.s Bumping your thread is agaist forum rules!!

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.