Solve Confusing Freight Transport Problem on Titan

[physikamateur]

Homework Statement

Freight transport on Titan is mostly by ship, with three types of ship called pangs, quizzers and roodles in common use. All three ships have the same shape and design but differ in size. The cargo capacity depends on the hold volume, while the number of crew required is proportional to the surface area of the deck. A quizzer and a roodle taken together have the same length as two pangs, and the crew of a quizzer is just sufficient to provide crew for two pangs and a roodle.

A fully loaded quizzer whishes to transfer all its cargo to smaller pangs and roodles, while minimising the number of crew required for the resultant fleet. How many pangs and roodles are needed ?

[Hint: Note that for objects of any shape the surface area is proportional to the square of the object's size, and the volume is proportional to the cube of its size.]

Please help

Thank you.

Homework Equations

The Attempt at a Solution

I tried using ratios, but it got very messy. I'm confident that ratio is the best method to solve this problem.

 

[cepheid]

Try Lp, Lq, Lr for lengths of the 3 ships respectively.

The statement about lengths tells you that

Lq+Lr=2Lp

What equation does the statement about crew sizes give you?

So you have 2 equations and 3 unknowns, meaning you can solve for any two lengths in terms of the third. This gives you the ratios you want.