### Brain Teasers

# Ship and Boiler

Math
Math brain teasers require computations to solve.

A ship is twice as old as its boiler was when the ship was as old as the boiler is now.

The sum of their ages is 21.

How old is the boiler, and how old is the ship?

The sum of their ages is 21.

How old is the boiler, and how old is the ship?

### Hint

Once you get your head around the wording, I think it's easy enough. Try and write down the equations for everything you know.### Answer

There is an age difference between the ship and the boiler, lets call it D. It will always be the sameSHIP = BOILER + D (1)

The SHIP = 2 * (what the BOILER was) (2)

BOILER NOW = BOILER's age then + D (3)

SHIP NOW + BOILER NOW = 21 (4)

There are now 4 equations with 4 unknowns which can be solved simultaneously To give :

Ship is 12

Boiler is 9

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## Comments

Right, I totally got that...

As a response to other people on the site, I do think the comment box is under-used! Tell me what you think!

I think this puzzle is harder than the 2.33 rating it has at the moment. I should have included the answers is not 14 and 7. I don't know why, but I think a lot of people jump for that answer...

I think this puzzle is harder than the 2.33 rating it has at the moment. I should have included the answers is not 14 and 7. I don't know why, but I think a lot of people jump for that answer...

beacuse the beging is so confusng! And don't beg for points!

I'm not begging, I'm wondering if it actually is that easy/hard to people, (the rating has since gone down) or if people just give a rating to get the point forthemselves without reading the question)

Obviously I don't know if something is easy or hard to everyone else, I just want to know. Feedback makes it a lot easier to write a better puzzle

Obviously I don't know if something is easy or hard to everyone else, I just want to know. Feedback makes it a lot easier to write a better puzzle

Ha ha ha , Cathalmcabbage asking for feed back. Tried that, he cried.

H ha ha ha Cathal begging for points ha ha ha It just gets better

H ha ha ha Cathal begging for points ha ha ha It just gets better

Aug 25, 2002

"There are now 4 equations with 4 unknowns which can be solved simultaneously To give :

Ship is 12

Boiler is 9"????

How does this work, how can unknowns suddenly become 12 and 9? shouldn't there at least be an explanation to how you got this?

Ship is 12

Boiler is 9"????

How does this work, how can unknowns suddenly become 12 and 9? shouldn't there at least be an explanation to how you got this?

A tongue-twister for the mind. Maybe it is just me, but my biggest problem was working out the scenario. The only thing for sure was that the ship's age was currently an even number.

I found this teaser easy and I didn't need any equations to solve it. Once you imagine the situation, it is clear that the boiler is 3/4ths of the ship's age. From there it is relatively simple.

correct me where i go wrong, but for the ship to be twice as old as the boiler, when the ship was as old as the boiler is now... that means when the ship was 9, it was twice as old as the boiler, making it 4.5.... but the boiler wouldve been 6 years old then... right? please, just inform me of my misstep, i will not be surprised to find out i messed it up, just am unaware as of now. i somehow dont think any whole number works... its between 12 and 13, i believe, though. 12.6, 8.4 actually is the correct answer. cause when the ship was 8.4, thats was 4.2 years before now, making the boiler 4.2

Let S stand for ship's age, B for the boiler's age, D for the difference between them, and B' for the boiler's age 'back when.'

Their combined ages are 21.

S + B = 21.

The ship is D years older than the boiler.

S = B + D.

D years ago the ship was as old as the boiler is now, and the boiler was D years younger.

B' = B - D.

The ship is twice as old as the boiler was 'back when.'

S = 2B' = 2B - 2D.

From the 2 equations defining S,

2B - 2D = B + D.

B = 3D.

Then, using either definition,

S = 4D.

Substituting these values in the first of my equations,

4D + 3D = 21.

7D = 21.

D = 3.

Their combined ages are 21.

S + B = 21.

The ship is D years older than the boiler.

S = B + D.

D years ago the ship was as old as the boiler is now, and the boiler was D years younger.

B' = B - D.

The ship is twice as old as the boiler was 'back when.'

S = 2B' = 2B - 2D.

From the 2 equations defining S,

2B - 2D = B + D.

B = 3D.

Then, using either definition,

S = 4D.

Substituting these values in the first of my equations,

4D + 3D = 21.

7D = 21.

D = 3.

let boiler's age now = x, ship's age now is x + n where n difference of their ages.

so when ship's age is the same as the boiler's age now (which is n years ago), boiler's age = x - n, ship's age now is x.

equation 1 : x + n = 2(x - n)

x = 3n

equation 2 : x + (x + n) = 21

2x + n = 21

2(3n) + n = 21

7n = 21

n = 3

therefore, x = 3n

x = 3(3)

x = 9 (boiler's age)

x + n = 9 + 3 = 12 (ship's age)

actually a simple problem involving 2 variables with with equations. main problem is understanding the wording of the teaser.

so when ship's age is the same as the boiler's age now (which is n years ago), boiler's age = x - n, ship's age now is x.

equation 1 : x + n = 2(x - n)

x = 3n

equation 2 : x + (x + n) = 21

2x + n = 21

2(3n) + n = 21

7n = 21

n = 3

therefore, x = 3n

x = 3(3)

x = 9 (boiler's age)

x + n = 9 + 3 = 12 (ship's age)

actually a simple problem involving 2 variables with with equations. main problem is understanding the wording of the teaser.

Break it down phrase by phrase. Say the age of the boiler WAS x. Ship is NOW 2x. y years go by.

Boiler is now (x+y).

Back then the ship WAS 2x-y=x+y {The boilers age now} x = 2y.

Adding ages 2x + (x+y) = 7y = 21 y = 3.

Ship is 2x = 4y = 12. Boiler is x + y = 9.

Like Pating I think it is good to keep it simple.

Boiler is now (x+y).

Back then the ship WAS 2x-y=x+y {The boilers age now} x = 2y.

Adding ages 2x + (x+y) = 7y = 21 y = 3.

Ship is 2x = 4y = 12. Boiler is x + y = 9.

Like Pating I think it is good to keep it simple.

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