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Question:

$$\begin{align} &\text{Joe has a sailboat.}&\\ &\text{His sailboat is twice as old as Joe was when his sailboat was as old as Joe is now.}&\\ &\text{Their age's combined is 56 years.}&\\ \end{align}$$

Here's my go at it, It's basically just solution by exhaustion:

$j= $ age of Joe, $\ s = $ age of sailboat, $\ y=$ young Joe, $\ p=$Sailboat in the past.

$$c = j+s = 56$$

$$p = j$$

$$x = s-j$$

$$y = p - x \implies y = j-x$$

$$s=2(j-x) \implies 2s=x+c$$ $$s-x=x+{s\over2}\implies x={s\over4} \implies$$ $$2s={s\over4}+c \implies s=32 $$ $$j+32=56 \implies j= 24$$

It looks very ugly, so I am wondering if there is any other, less messy ways of solving problems of such nature?

JohnWO
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  • I don't think so. One reason why I hate this kind of questions is that it merely involved untangling the exact phrasing, which then leads to tedious but direct equations. – Calvin Lin Jun 23 '13 at 18:17

1 Answers1

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Joe's present age: $j$

Sailboat's present age : $s$

Let's look at the third sentence. It gives $j+s = 56.$

Now for the second: 'When his sailboat was as old as Joe is now, his sailboat's current age is twice as old as Joe's was'.

It's given that when the age of the sailboat was $j$, the sailboat's age is twice as old as the age of Joe at that time. What was Joe's age at that time? The sailboat was $j$ years old and that was $s-j$ years ago, so Joe's age $s-j$ years ago was $j-(s-j) = 2j-s$.

Thus the second sentence gives $s=2(2j-s)$ or $3s = 4j$.

Solving gives the result you got.

I can't really suggest much about how to solve these kind of problems due to the various ways these questions can be asked in but the general idea is to just do it systematically by evaluating the information each sentence gives you and rephrasing some sentences to make them easier to understand while you try to solve it.

Alraxite
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