The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 34 barrels of oil in traveling 60 miles at 20 mi/h. How many barrels of oil are used when the ship travels 32 miles at 23 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.

Step-by-step explanation:

Joint variation has the equation

y = kxz

k is the constant of variation and needs to be solved for using the initial conditions, then filled in later to another equation related to the given info to solve for something else.  We are given y = amount of oil used, x = distance traveled, z-squared is the speed.  Our equation looks like this, to be exact:

Filling in with the initial conditions:

which gives us the

k = .0014166667

Now we need to find the amount of oil used, y, under other circumstances, but this time we have our k.

which gives us that the amount of oil used, when rounded to the tenths,

y = 24.0 barrels