Today I’d like to share a couple of quick and easy calculations that you will find on the Coast Guard exams. How to solve for fuel conservation by either time or distance. There is a formula for each and they are not found in the reference materials in the exam room, so they do need to be memorized. The questions in the exams will then require us to rearrange these equations to solve for our desired variable, but that is simple algebra, which we should all be familiar with already. So, let’s take a look at these two formulas

### Solving for fuel conservation by distance:

#### $\frac{NEW\ CONSUMPTION}{OLD\ CONSUMPTION} = \frac{NEW\ SPEED^2\ \times\ NEW\ DISTANCE}{OLD\ SPEED^2\ \times\ OLD\ DISTANCE}$

Now, a couple of mnemonics that help me remember these formulas:

• New is always the numerator. NEW-merator. Get it? Corny I know. Alternatively it’s like stacking something. New things go on top of the old things.
• For whether to cube or square the speed, I think of the right side of the forumla needing to have three items. It’s either speed x speed x speed (cubed) or if we introduce distance, it can be speed x speed (squared) x distance. Either way there are three parts to the right side of the equation.

Just a couple of suggestions for mnemonics, feel free to use whatever works for you, but definitely try to come up with something like this, anything that makes it easier to recall when you’re in that exam room.

So, let’s work through a few problems. We will solve one for speed, one for distance, and one for consumption.

### CG # 03267

Your vessel arrives in port with sufficient fuel to steam 726 miles at 16 knots. If you are unable to take on bunkers, at what speed must you proceed to reach your next port, 873 miles distant?

• A – 14.6 knots
• B – 15.1 knots
• C – 16.3 knots
• D – 16.8 knots

### CG # 03254

You have steamed 746 miles at 14.0 knots and consumed 152 tons of fuel. If you have 201 tons of usable fuel remaining, how far can you sail at 10 knots?

• A – 1381 miles
• B – 1934 miles
• C – 2263 miles
• D – 2707 miles

### CG # 03291

While steaming at 19.5 knots, your vessel burns 297 BBLS of fuel per day. What will be the rate of fuel consumption if you decrease speed to 15 knots?

• A – 135 BBLS
• B – 176 BBLS
• C – 229 BBLS
• D – 243 BBLS

Follow along in this video to see how we will rearrange our equations and solve these problems.