Scale model submarine length in inches or feet

[Dagenais]

I know it is an easy problem, but I want to know if I have the answer correct.

I'm confused whether the answer is already in inches, or is still in feet.

The story problem is:

The larget submarines in the United States Navy are of the Ohio class. Each submarine is 560 feet long.

You purcahse a scale model of one of the submarines. The package states the scale of 1 inch: 16 feet. What is the length of the completed model?

So to solve, I put:

x/560ft = 1/16ft

x=35

OR is x = 420 inches? Is 35 already in inches, or is it still feet and needs to be converted (which results in 420 inches).

 

[Hurkyl]

Well, if you put the units on all of the terms that went into that ratio, your answer would have the units on it!

 

[Dagenais]

I did, and it is 1inch/16ft and xinches/560feet.

Doesn't help much, since I have both inches and feet.

 

[Hurkyl]

Is "x" supposed to be "length of the model" or "number of inches in the length of the model"? (The way you wrote the ratio, it's the latter)

I did, and it is 1inch/16ft and xinches/560feet.

Doesn't help much, since I have both inches and feet.

Why doesn't it help? Surely you can do some sort of canceling, or if not, make some sort of substitution...

 

[Dagenais]

So I was right, 35 inches is the answer?

 

[Integral]

You have
$$\frac {1 inch} {16 ft} = \frac {x inches} {560 ft}$$

when you multiply both sides by 560ft you get

$${x inches} = \frac {1 inch * 560 ft} {16 ft}$$


the feet cancel leaving only inches.

 

[Dagenais]

I did it on my calculator.

I completely missed that whole 2nd step. I kind of just typed in the equation in my calculator.

So 35 is right, thanks!

BTW, how did you write those equations? I recall instructions about it on the forums, before new forums were added but I can't find them.

 

[Integral]

click on the formulas to see the text entered to create them.

note that color does not matter.

 

[Hurkyl]

P.S. IMHO, it makes it easier to understand things like this if you solve the problem by first defining your variable x as "The length of the completed model"

Then the ratio is

1 in / 16 ft = x / 560 ft

And when you solve, you're left with

x = 35 in