[superprismatic]

Here's a cute little word problem which, although

not difficult, is very hard for most people to parse:

"The ship is twice as old as the boiler was when the

ship was as old as the boiler is now. What are the

relative ages of the ship and the boiler?"

It can melt the neurons on some teenagers!

[Guest]

Neurons were melted in this brain... however when I made it simpler in my head I was working around 5's so I can trial and error my way to the answer.

...the ship is 20 and the boiler is 15. Reason being the ship is 5 years older, so when the ship was 15 the boiler was 10, which is half of 20 (the ships current age).

But I think this should be left open until someone comes up with a formula. My math skills have rusted over, but I believe it would be a function? Like an equation involving f(x)?

Edited August 3, 2009 by Shadax

[Guest]

they are the same age

[Guest]

But I think this should be left open until someone comes up with a formula. My math skills have rusted over, but I believe it would be a function? Like an equation involving f(x)?

The ratio of the ship/boiler is 4/3.

Mathematically (subscripts are for "now" and "then"):

S_n=2B_t

S_t=B_n

S_n-S_t=B_n-B_t

Substituting the boiler variables for the ship variables in the third equation, we get this:

2B_t-B_n=B_n-B_t

2/3B_n = B_t

And substituting that into the first equation:

S_n=4/3B_n

[Guest]

Here's are my thoughts on what the formula would look like.

4/3x Current Ship Age; x = prior ship age/current boiler age; 2/3x = prior boiler age. Therefore, 20,15,10 work; as does 8,6,4 etc.

[Guest]

Here's are my thoughts on what the formula would look like.

4/3x Current Ship Age; x = prior ship age/current boiler age; 2/3x = prior boiler age. Therefore, 20,15,10 work; as does 8,6,4 etc.

Ah, see now that makes good sense but I did not think far enough outside the box for that one.

It's Monday

[Guest]

Here's what I got using a formula:

x₁=Ship 'then'

x₂=Ship now

y₁=Boiler 'then'

y₂=Boiler now

x₂=2y₁ and x₁=y₂ obviously.

Because the time between 'then' and now is the same for the boiler and the ship x₂-x₁=y₂-y₁.

x₂=2y₁ so y₁=x₂/2.

Substituting we get x₂-x₁=y₂-x₂/2.

We can then rearrange the above formula as y₂=1.5x₂-x₁.

Since x₁=y₂, we can substitute the above formula as x₁=1.5x₂-x₁.

Rearranging gives 2x₁=1.5x₂ and then x₁=0.75x₂.

Again, since x₁=y₂, y₂=0.75x₂

So Shadax is correct!

damn, too slow!

Edited August 3, 2009 by The Zealous Zebra

[Guest]

here's a math solution

s= ship, b= boiler, y=some years ago

s = 2(b-y)

s - y = b or y= s-b

using it

s = 2 (b - (s- b) )

or 3s = 4b

b = 3/4s

Edited August 4, 2009 by chirkut

[Guest]

I think it is (ship/boiler)

3/2

[Guest]

The boiler is 3/4 the age of the ship. This would, indeed, cause many folks some trauma.

[Guest]

the boiler is 3/4 the boat.

boaTNow=2boileRThen

TT=RN

TN-RN=TT-RT

TN-RN=RN-1/2TN

3/2*TN=2*RN

[Guest]

This is easy. The ship is 1.5 times older than the boiler.

Proof by example.

If the boiler is now 10, when the ship was 10 (twice the boiler's age) the boiler was 5. So the ship is 5 years older than the boiler. Thus, since the boiler is now 10, the ship must be 15.

If the boiler is now 20, when the ship was 20 (twice the boiler's age) the boiler was 10. So the ship is 10 years older than the boiler. Thus, since the boiler is now 20, the ship must be 30.

Using the ratio (ship age):(boiler age) we have 15:10 and 30:20

Those both reduce down to 3:2 which means the ship is 1.5 times older than the boiler.

Edited August 4, 2009 by Kriil

[Guest]

Oops, that was nit-picking the wording so I have erased my posting. Sorry.

Edited August 4, 2009 by Kriil

[Guest]

I just realized that I solved - "The ship WAS twice as old as the boiler was when the

ship was as old as the boiler is now." - instead of "The ship is..."

Ah semantics.

[Guest]

Neurons were melted in this brain... however when I made it simpler in my head I was working around 5's so I can trial and error my way to the answer.

...the ship is 20 and the boiler is 15. Reason being the ship is 5 years older, so when the ship was 15 the boiler was 10, which is half of 20 (the ships current age).

But I think this should be left open until someone comes up with a formula. My math skills have rusted over, but I believe it would be a function? Like an equation involving f(x)?

I think the formula will go as follows

Lets consider age of ship & boiller as X & Y resp.

Then X= 2 (Y-(X-Y))

X = 2 * (2Y-X)

X = 4Y-2X

3X = 4Y

y=3X/4

Now you can put up any value of X & Y

eg:- X=100 then Y = 75