Friday Puzzler -- How Old?

Re: Friday Puzzler -- How Old?

Larry Barrett

Algebra is not helping, so far. But trial and error says Adam is a little under 38 and Bob is a little over 25.

No, but...

Alex Y

if I had asked a different question that would have been the answer ;-)

Re: No, but...

Larry Barrett

If I now understand the question correctly, three times Bob's current age is equal to two times Adam's current age.

Correct!

Re: Friday Puzzler -- How Old?

Walleye Tom

Linear equations make what is left of my burned out brain want to ooze from my ears and nostrils.

As a matter of fact, just from reading your question and thinking about Bob and Adam, I am going to make a very strong Cocktail and get counseling from the Porn section of the Internet.

Re: Friday Puzzler -- How Old?

Larry Barrett

Hi Walleye Tom

It was (still is, every time I read it) hard to untangle this puzzle.

Here are the equations I came up with. You will still need to do some algebra to get to an answer.

Lets say that Adam is x years older than Bob. So A=B+x.

Now,

When Bob gets to be as old as Adam is, Bob's and Adam's ages will add to 63.

So Bob gets to be as old as Adam is means B will be x years older than now, and when B is x years older, A is also x years older,

So this equation is (B+x)+(A+x)=63.

and

Adam is three times as old as Bob was when Adam was as old as Bob is.

So when Adam was as old as Bob is means A was x years younger, and when A was x years younger, B was also x years younger,

So this equation is A=3(B-x).

The wording

Alex Y

Larry and Tom, I agree that the most difficult part of this puzzle is getting your mind around what the wording means as you try to set up the equations. I added modifiers to help me when I was solving this.

Adam is now three times as old as Bob was at a time in the past when Adam was as old as Bob is now.

When, at some future date, Bob gets to be as old as Adam now is, Bob's and Adam's ages at that future date will add to 63.

How old are Adam and Bob now?

Doing that got me to focus on the three dates as of which ages were being discussed, and see that those times were now and +/- the difference in ages ("x" in Larry's setup).